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Super-Resolution Imaging Using MultiElectrode CMUTs: Theoretical Design and Simulation Using Point Targets Wei You, Student Member, IEEE, Edmond Cretu, Member, IEEE, and Robert Rohling, Senior Member, IEEE Abstract—This paper investigates a low computational cost, super-resolution ultrasound imaging method that leverages the asymmetric vibration mode of CMUTs. Instead of focusing on the broadband received signal on the entire CMUT membrane, we utilize the differential signal received on the left and right part of the membrane obtained by a multi-electrode CMUT structure. The differential signal reflects the asymmetric vibration mode of the CMUT cell excited by the nonuniform acoustic pressure field impinging on the membrane, and has a resonant component in immersion. To improve the resolution, we propose an imaging method as follows: a set of manifold matrices of CMUT responses for multiple focal directions are constructed off-line with a grid of hypothetical point targets. During the subsequent imaging process, the array sequentially steers to multiple angles, and the amplitudes (weights) of all hypothetical targets at each angle are estimated in a maximum a posteriori (MAP) process with the manifold matrix corresponding to that angle. Then, the weight vector undergoes a directional pruning process to remove the false estimation at other angles caused by the side lobe energy. Ultrasound imaging simulation is performed on ring and linear arrays with a simulation program adapted with a multi-electrode CMUT structure capable of obtaining both average and differential received signals. Because the differential signals from all receiving channels form a more distinctive temporal pattern than the average signals, better MAP estimation results are expected than using the average signals. The imaging simulation shows that using differential signals alone or in combination with the average signals produces better lateral resolution than the traditional phased array or using the average signals alone. This study is an exploration into the potential benefits of asymmetric CMUT responses for super-resolution imaging.

I. Introduction

C

apacitive micromachined ultrasonic transducers (CMUTs) have several potential benefits over traditional piezoelectric transducers in some applications. For example, CMUTs have been recently used in ring arrays for forward-looking intracardiac echocardiography (ICE) and intravascular ultrasound (IVUS) imaging applications [1], [2]. When a ring array is used to image targets at a distance much larger than its aperture, classic phased ar-

Manuscript received April 30, 2013; accepted July 19, 2013. This work is supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) under grant STPSC 356839-07. The authors are with the Department of Electrical and Computer Engineering, University of British Columbia, Vancouver, BC, Canada (e-mail: [email protected]). R. Rohling is also with the Department of Mechanical Engineering, University of British Columbia, Vancouver, BC, Canada. DOI http://dx.doi.org/10.1109/TUFFC.2013.2827 0885–3010/$25.00

ray imaging approach produces a broad beam and high side lobes [3], therefore synthetic aperture array imaging with various techniques such as aperture weighting [4], [5] and spatial/temporal coding [6], [7] have been applied to improve the image quality. These techniques can add a considerable computational load that limits the overall frame rate in certain implementations [2]. Fast imaging using a broad beam or plane wave transmission [8]–[10] may improve the frame rate substantially but further degrades the image resolution. Transmitting plane waves from multiple angles [8] yields quality comparable with the focused B-mode images. In [2], this technique is considered for integration into a CMUT ring array system. In a related research direction, super-resolution imaging techniques have also been proposed to overcome the diffraction limit in ultrasound imaging [11]. Various approaches have been developed in this field [12]–[17]. qTONE [13] is one example based on radar and sonar literature [18]. This method first transmits a plane wave, and records the temporal channel responses of each hypothetical target in the region of interest (ROI) to form a manifold matrix. During the imaging process, it solves a maximum a posteriori (MAP) problem to obtain the weights of each hypothetical target. To make an accurate estimation of the weights, especially in the case of a small aperture array with a broad beam pattern and high side lobes, millions of calibration targets are required, resulting in high computation complexity. In this work, we propose a super-resolution imaging method and demonstrate it on phased ring and linear arrays. The purpose of the work is to study the potentials of using asymmetric modes of CMUTs for super-resolution imaging. The proposed method is based on the differential received signals obtained by a novel multi-electrode CMUT structure. Because of the clamped-plate structure of a CMUT cell, off-axis targets can excite asymmetric resonant modes on CMUTs, which could be captured by monitoring the difference of the signals collected on partial (left and right) electrodes of a CMUT cell. This concept was proposed in [19] for the estimation of direction of arrival (DOA) of off-axis targets. The present work extends the concept to super-resolution imaging. The differential received signals from all CMUTs form decorrelated temporal patterns for different beam directions and lead to a more accurate estimation result of reflector locations than using the same amount of received data averaged on

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the single electrode. Thus the new method can potentially improve the image resolution compared with the phasedarray method, and is a low-cost alternative to the previous manifold matrix-based super-resolution methods. Section II briefly explains the source of the resonant components in the differential received signals from a mode decomposition perspective. Section III described the new super-resolution method using the unique signature of the differential signal. The imaging simulation results using a multi-electrode CMUT ring array and a linear array are shown in Section IV, and the trade-offs of the method are discussed in Section V. II. Multiple Vibration Modes During CMUT Reception A. Regular Mode of Operation A CMUT cell typically consists of a thin doped silicon plate that is tens of micrometers in diameter suspended on its edge. A submicrometer air or vacuum gap between the plate and the substrate provides the dielectric space for capacitive actuation and sensing. A high dc voltage is usually applied between the plate and the substrate to increase the transduction sensitivity. In transmit mode, an ac voltage is superimposed to cause the plate to vibrate and transmit ultrasonic pressure waves into the tissue; in reception, the plate vibrates with the incoming acoustic pressure, which converts the pressure signal to the mechanical movement or the change in gap capacitance. There has been extensive research work on the fabrication, modeling, and application of CMUTs [20]–[24]. The hundreds of CMUT cells in an array are usually excited with the same voltage, and each of them is modeled considering only the first vibration mode shape of a plate [25]. In an immersion environment typical for medical ultrasound, CMUTs show a broadband behavior, which is one of the advantages over its piezoelectric counterpart [26]. B. Asymmetric Mode of Operation The CMUT behavior can be analyzed using the mode superposition method both theoretically [27], [28] and using a multi-modal equivalent circuit model [29]. When the force acting on the CMUT plate is nonuniform, the resulting CMUT behavior is the superposition of axially symmetric and asymmetric mode shape components. Higher order symmetric mode components were reported as undesirable dips in the frequency spectrum [30], and higher order asymmetric components were observed as a result of the acoustic crosstalk [31] or manufacturing defect of the CMUT cell [32]. There has been work on making use of the higher order symmetric modes. For example, in [30], additional mass loadings are placed on the CMUT membrane to adjust the frequency of the third mode, and the

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harmonic signal of this mode is selectively detected from the side electrode of a multi-electrode structure [33] to enable harmonic imaging. In this work, we propose an imaging method by leveraging the resonant behavior of the second vibration mode (asymmetric mode). We have investigated the principle and possible applications of the asymmetric mode of CMUTs in [27] and [34]. The symmetric and asymmetric mode displacement is graphically shown in Fig. 1. Asymmetric mode components exist when a non-axisymmetric force is exerted on the membrane, e.g., a difference in electrostatic forces exerted on the left and the right part of the membrane in transmission, or difference in acoustic pressure in reception. Other higher-order modes can exist, but they are much farther away from the operational frequency band, typically have lower energy, and can be filtered out using a band-pass filter if necessary. The asymmetric mode is a local exchange of kinetic energy between the parts of the CMUT membrane involving only the near surface fluid, and does not radiate acoustic pressure [28], [35]. Although the displacement or velocity sensed on the entire plate is non-resonant (thus making dips in the spectrum), the local measurements integrated on each half of the membrane appear to be resonant and in opposite phase with one another. The proposed method makes use of the relations between the acoustic pressure difference and the differential received signal between the left and right halves of the membrane, which is a direct reflection of the asymmetric mode. A novel CMUT structure with half-membrane-sized electrodes described in [34] is used to separately obtain the signals from the left and right parts of the electrode. C. Average and Differential Received Signals From Multi-Electrode CMUTs Fig. 2 shows an example of the average displacement of the whole CMUT membrane, the left part, and the right part of the membrane resulting from a simulated large-angle off-axis acoustic pressure source from the finite element simulation (see Section IV-A for details). The dif-

Fig. 1. Displacement amplitude of a circular CMUT membrane under an external pressure field with no excitation voltage. (a) Symmetric vibration mode resulting from uniform external pressure. (b) Asymmetric vibration mode resulting from different levels of acoustic pressure on the left or right side of the membrane [27].

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A. Imaging With a Ring Catheter In [2], a ring catheter made of CMUT elements was described and several imaging methods using the catheter were compared. In summary, because of the ring geometry, plane wave transmission (flash imaging) results in poor off-axis image quality, and the phased array beamforming method generates high side lobes. A synthetic phased array with Hadamard coding and aperture weighting provides the best image quality and decent frame rate, but has an immense computational load. B. Super-Resolution Imaging Using Differential Received Signals Fig. 2. Average displacement of the whole membrane, left and right part of the membrane subjected to an acoustic wave from a large off-axis angle.

ferential signal is then a harmonic signal with the resonant frequency of the asymmetric mode, which may be deemed as unwanted in regular imaging, but is used in our method for super-resolution imaging.

III. Efficient Super-Resolution Imaging Based on Differential Received Signals of CMUTs The goal of this section is to develop a super-resolution image method with relatively low computational complexity.

The difficulties with catheter imaging is the off-axis image quality fall-off in fast imaging, and high side lobes in phased array imaging. In this study, we propose a focused super-resolution imaging method with a directional pruning step, and compare the performance between using average received signals and differential received signals. The workflow of the method is shown in Fig. 3. 1) Manifold Matrices and Estimation of Imaging Target Locations: The proposed approach first defines a grid of hypothetical imaging targets in the ROI, and constructs manifold matrices V, similar to the approach in [12] and [13]. Each column of V is the concatenation of the T temporal received samples at each of the N array elements for each hypothetical target. The matrix consists of LP columns, L and P being the number of hypothetical targets

Fig. 3. Workflow of the proposed method. [A] Manifold matrices construction. [B] MAP estimation of weight vectors. [C] Pruning of weight vectors. [D] Image reconstruction.

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Fig. 4. (a) Manifold matrix constructed from Savg. (b) Manifold matrix constructed from Sdiff. The vertical axis represents L hypothetical target locations in angular directions, and the horizontal axis represents NT temporal received samples.

in two dimensions. When new signals are received and concatenated into an NT vector, the target locations and the amplitudes (weights) can be estimated by an iterative method [13]:

f k +1 = C f V H (VC f V H + C n)−1x , (1) k

k

where V is the NT × LP manifold matrix, f is an LPdimension vector representing the weights of the hypothetical targets, C is the covariance matrix of f, Cn is the noise covariance matrix, and x is the new NT-dimension concatenated temporal signals received at all N elements. 2) Temporal Signature of Differential Received Signals: As discussed in Section II, the signal received at the left and right electrode alone (SL and SR) is a superposition of the broadband, symmetric mode, and the narrowband, asymmetric mode, which shows a longer ringing effect than the regular CMUT received signal. The regular received signal, which is the average signal on the left and right electrodes, Savg = (SL + SR)/2, appears as time-delayed pulses across all elements/cells when concatenated [Fig. 4(a)], and the time delays are tiny for a small aperture transducer, whereas the differential signals across all the elements/cells, Sdiff = SL − SR, have a unique amplitude signature [Fig. 4(b)]. A map of correlation coefficients of the LP columns of the manifold matrices Vavg and Vdiff are shown in Fig. 5, where the pixel brightness is mapped to the range of the correlation coefficients. The mapping shows a wide band of high correlation coefficients around the diagonal for Vavg, and only a narrow band for Vdiff. This means that the columns of Vdiff are more decorrelated than those of Vavg; therefore, when Sdiff and Vdiff are used, (1) can be solved more accurately because of the greater separation of the manifold vectors in space. 3) Multi-Focus Manifold Matrices Construction: Plane wave transmission suffers from lower resolution and image contrast than focused transmit and receive beamforming

[8]. To obtain higher resolution and reduce side lobes, we propose a focused super-resolution imaging approach with a trade-off in memory space. One NT × LP manifold matrix is constructed off-line for each of the M scan lines or angular positions (Fig. 3, Step [A]). A set of manifold matrices are constructed for both the average and differential received signals:

V avg = {Viavg, i = 1, 2,..., M }

(2) V diff = {Vidiff, i = 1, 2,..., M }.

4) Multi-Focus MAP Solution of the Weight Vector: During the imaging process, the array focuses at multiple angular positions in transmission and performs beamforming in reception. After the reception from the ith angle, an iterative MAP process similar to (1) is performed to obtain the optimal weight vector fi (Fig. 3, Step [B]). 5) Pruning of Weight Vectors: Next, a directional pruning step is applied to fi to further reduce the effect of side lobes. fi is the estimated weights of all hypothetical targets in the grid when the beam is focused at the ith angle. It includes the estimated weights within the ith angle resulting from the highest energy of main lobe of the transmit/ receive beam, and the weights at other angles resulting largely from the energy of the side lobe. When fi is used

Fig. 5. (a) Correlation coefficient map of Vavg. (b) Correlation coefficient map of Vdiff. The brightness of the pixels is mapped to the coefficient values.

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Fig. 6. Directional pruning process. For the weight vector estimated while the array steers to the ith angle θi, keep the values corresponding to θi and set the values at other angles to zero as they tend to be false estimates. Note that multiple values for different axial locations at θi are all kept.

for the reconstructing the current scan line, the mixture of main lobe energy and side lobe energy will both contribute, causing false images. Because only the echoes from the targets within the current scan line are needed for the current reconstruction, and echoes from targets outside this scan line have also been identified as weights at corresponding positions, we set to zero the weights of the targets outside the current ith focal angle, keeping only the estimates at positions corresponding to the ith angle (Fig. 3, Step [C]). The resulting pruned weight vector is defined as fp,i. A detailed illustration of the pruning process is shown in Fig. 6. A weighted average of n neighbors of the current focal angle can be used to improve robustness and reduce false negatives.

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the result section, this operation removes false positives from both the solutions. The methods using the proposed imaging process with the average received signal (Savg), the differential received signal (Sdiff), and the hybrid weight vector will hereafter be denoted super-resolution average (SRA), super-resolution differential (SRD), and super-resolution hybrid (SRH), respectively. The goal is to show that SRD and SRH improve the image quality over the traditional phased array as well as SRA. 8) Scaling and Interpolation: In a regular phased array, additional scan lines can be interpolated from physically acquired scan lines to improve the resolution. Scan line interpolation can also be achieved in our technique. When the beam is steered to an angle, all weights in f are estimated. The RF signals from the targets falling between the scan lines can be interpolated by combining the weights estimated from the neighboring scan lines. Assume the scan lines only sample the hypothetical target matrix at every other angle, i.e., the beams are only steered to θi−1, θi−1, θi−3, …, one way to interpolate the lines at θi, θi+2, … could be

avg i i x i = (Viavg −1 f p,i −1 + Vi +1 f p,i +1)/2, (4)

where xi is the RF data for the interpolated scan line, f p,i i −1 and f p,i i +1 are the weight vectors estimated at θi−1 and θi+1, pruned only to keep the elements at θi. The 6) Image Reconstruction: The image is then recon- weight vectors are converted to RF data by multiplying structed using the pruned fp of each scan line with the the manifold matrices of their respective angle, Viavg −1 and manifold matrix of the average signal: Viavg , and averaging to construct the interpolated line. +1

x i = Viavg f p,i , (3) IV. Simulation and Results

where xi is the resulting RF data of the ith scan line, and fp,i is the pruned fi of the ith scan line (Fig. 3, Step [D]). Instead of directly displaying the weights of the hypothetical targets as brightness in the image, our method attempts to preserve some of the texture information in the RF data by weighting the manifold RF data in the B-mode image reconstruction. The scan lines are envelope detected, log-compressed, and scan converted to form an image (Fig. 3, Step [E]).

This section shows the simulation and results of the proposed imaging method using both finite element modeling (FEM) and the ultrasound field simulation program Field II [36]. A miniature ring array geometry was tested first, followed by variation of frequency of the ring array, as well as a linear phased array.

7) Hybrid Method Using Weight Vectors From the Average and Differential Signals: Because the signature of the regular concatenated channel data largely relies on the temporal delays between different locations of the hypothetical targets, the average received signals are well-suited for detecting targets along the axial direction. On the other hand, the differential signals have a more distinct signature between angles, providing better lateral discernibility. We propose to fuse these two advantages by taking the element-wise product of the two weighting vectors: diff fp,i,j = f pavg ,i, j × f p,i, j , where fp,i,j is the jth element of the pruned f vector of the ith scan line. As will be shown in

First, the received signals on the multi-electrode CMUT cell in response to acoustic sources from different angles were simulated with FEM software, (Comsol Multiphysics, Comsol Inc., Burlington, MA). The FEM model (Fig. 7) consists of a single CMUT cell with a polysilicon membrane that has a diameter of 94 μm and a thickness of 1.5 μm, and a vacuum gap of 0.75 μm, the same dimensions as the novel multi-electrode CMUT structure we fabricated [34] (Fig. 8). A 100 V dc bias voltage is applied at the bottom of the membrane, and the acoustic field is a 1-mm-long cylinder filled with viscous fluid (μ = 5.0 Pa·s) with sound-hard boundary on the peripheral and

A. FEM Simulation

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S = S sym + S asym = Pavg ∗ IR sym + Pdiff ∗ IR asym, (6)

Fig. 7. Finite element model simulating multiple physical domains of a CMUT cell.

radiation boundary at the end, simulating a CMUT cell vibrating in an array. The receiving scenario is analyzed in the FEM. The incoming plane wave pressure pulse P from an angle ϕ is simulated by applying a 10-ns Gaussian-shaped unipolar pulse with a continuous angle-dependent time delay across the CMUT cell membrane:

P = P0(t − (l + R)/(2R)t 0 sin(φ)), (5)

where P0 is a constant pressure, l is the lateral distance, R is the radius of the CMUT cell, t0 = 2R/c, where c is the speed of sound. The differential displacement on the left and right halves of the membrane, and the average displacement of the whole membrane are measured. The frequency domain average and differential signals are shown in Fig. 9. B. Ultrasound Imaging Simulation We revised the CMUT version of Field II so that each half of the CMUT membrane is a standalone unit of actuation and reception. The receiving impulse responses of the symmetric mode and the asymmetric mode, defined as the displacement or capacitance response to an acoustic pressure impulse, are extracted respectively from the FEM simulation. Assuming that the superposition of the two modes is linear, we have the following equation:

where S is the received signal, i.e., displacement or capacitance, Ssym and Sasym are the symmetric/asymmetric components. Pavg and Pdiff are the average/differential pressure on the left and right parts of the membrane, IRsym and IRasym are symmetric/asymmetric impulse response in reception, and ∗ denotes convolution. As a simplification, the asymmetric impulse response is chosen so that the ratios of Sasym between a few small angles in Field II simulation align with those of the FEM simulation. Examples of the symmetric and asymmetric impulse responses of the membrane displacement are shown in Fig. 10. 1) Simulated Ring Array and Imaging Targets: A ring array consisting of 48 CMUT cells with the aforementioned dimensions are constructed in Field II to demonstrate the new method (Fig. 11). The array has dimensions similar to the one fabricated in [2]. The diameter of the cells is 94 μm, and the radius of the ring is 0.8 mm. The static displacements of the individual CMUT cells in the Field II simulation are set from a cell profile extracted from an FEM simulation in which the dc bias voltage is 100 V. The CMUT cells have a central frequency of 1.8 MHz when operating in the symmetric mode in immersion, and a resonant frequency of 2.7 MHz in the asymmetric mode. The ring array is excited using three cycles of a 3 MHz sinusoid, and the imaging targets are at depths of 18 to 23 mm. 2) Extracting Differential Received Signals: For both offline manifold matrix construction and the imaging process, the CMUT ring array is excited with symmetric voltages, and the average and differential received signals from the targets are recorded as Sdiff = SL − SR, and Savg = (SL + SR)/2, where SL and SR are the received signals on the left and right halves of the CMUT membrane. 3) Manifold Matrix Construction: The manifold matrices are constructed using 126 targets in an ROI centered around z = 20 mm. There are 21 targets in angular direction from −20° to 20° with 2° separation, and 6 targets in axial direction from 18 mm to 23 mm with 1 mm separation. For both Savg and Sdiff, a manifold matrix set is

Fig. 8. (a) Top view of the CMUT cell layout with two and four electrodes. (b) Top view of part of the layout of the fabricated CMUT array.

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Fig. 9. Frequency domain average and differential received signals for different source angles from the FEM simulation results.

calculated by focusing at each of the 21 angular directions at z = 20 mm and stored in the memory. To reduce the NT-dimension row space of the matrices, responses of cells at the same lateral position in the ring are averaged, and the responses are recorded for every other cell in the lateral direction, thus making the rows a concatenation of 12 channel data. The sampling rate of the temporal signals was set to 1000 MHz in all acoustic field computations to avoid any delay-quantization error, and was later reduced to 10 MHz for the construction of the matrix and the subsequent estimation. 4) Weight Vector Computation and Image Formation: In an imaging simulation, point targets were placed in the ROI, and the ring array transmits and receives with 21 focal points consecutively. For each transmit/receive, the f vector is computed and pruned, and an RF scan line is reconstructed using the method described in Section III. This is done to preserve the continuous grayscale variation of an ultrasound image. The scan line matrix is then envelope detected, log-compressed, and scan-converted into a sector image. C. Comparison of Phased-Array Imaging and the Proposed Method The TX/RX beam profile of the ring array at z = 20 mm when focusing at 0° and 20° are shown in Figs. 12(a) and 12(b), respectively. The side lobes contribute to the smeared appearance during classic phased-array imaging. The idealized image of each simulated phantom is reconstructed assuming that imaging is done with the same number of angles (scan lines) as the proposed method, and the elements in fi corresponding to the true targets at θi have the value 1, and others being 0; therefore these images show interpolation effects between the scan lines. The phased array beamforming is done by focusing the ring array at 21 focal points without further processing. The imaging results for a simulated phantom of two columns of point targets 10° apart are shown in Fig. 13. This set of results shows that SRA provides superior lateral resolution to the conventional phased array beamforming and good axial resolution. SRD has a slightly worse axial

Fig. 10. Symmetric and asymmetric receiving impulse responses of membrane displacement.

resolution compared with SRA but good lateral resolution, with some false positives. SRH gives good axial and lateral resolution. For comparison, the imaging results of the same targets but calculated using a coarser hypothetical point target grid (9 × 6) are shown in Fig. 14. To show a more rigorous imaging scenario, a simulated phantom with half the spacing of the hypothetical targets is used, and the result in shown in Fig. 15. In this test, SRA misses the targets of some angles, and SRD detects some false positives in the axial and lateral directions but is capable of capturing all the targets. SRH removes some false positives, but does not recover the missing ones. Another test is performed with a simulated point targets phantom with the first two targets 10° laterally and 2 mm axially apart, and three bottom ones 10° laterally apart at z = 22 mm, as shown in Fig. 16. SRA shows better resolution than phased-array beamforming, SRD provides better estimation results than SRA, and SRH gives the best image quality. As shown in Fig. 12, the full-width at half-maximum (FWHM) beam width at the focal point is 5 mm. All of these imaging results show that the proposed methods (SRA, SRD, and SRH) are able to distinguish lateral targets within this beam width, which means our methods can achieve super-resolution in the lateral direction.

Fig. 11. Ring array with 48 CMUT cells constructed in Field II.

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Fig. 12. (a) TX/RX beam profile at 20 mm when focusing at 0°. (b) TX/RX beam profile at 20 mm when steering to 20°.

We measured the performance of the new method using an SNR value calculated as follows: Two binary masks defining the signal area and the noise area are created using the idealized B-mode image. The signal area includes the positions of expected targets in the idealized image (bright positions). The noise area includes the positions other than the expected targets (dark positions). The SNR of a new B-mode image is computed as the mean grayscale level in the signal area versus the mean grayscale level in the noise area. The SNR definition is similar to the signal window and noise window used in [2]. The SNRs of the B-mode images produced of the simulated phantoms shown in Figs. 13–16 by the phased array, the SRA method, the SRD method, and the SRH method are listed in Table I.

The results show that SRH produces the highest SNR among all methods, except for Fig. 15, in which both SRD and SRH generate more false positives than SRA, thus lowering SNR. The SNR for the result with a coarse target grid (Fig. 14) listed on the last row of Table I is not meant to be directly compared with the other rows, because it was calculated against its own idealized image with a larger interpolation effect. This row of SNR shows that with lower number of calibrated targets, SRD and SRH still produce higher SNR than the phased array, whereas SRA performs even worse than the phased array. This means that SRD and SRH can improve image quality over the phased array with a coarse calibrating target grid and are still relatively computationally efficient methods.

Fig. 13. Imaging results for two columns of point targets, calculated with manifold matrices of 21 × 6 hypothetical targets. (a) Idealized B-mode image. (b) B-mode image result using phased array beamforming. (c) B-mode image result using SRA. (d) B-mode image result using SRD. (e) Bmode image result using SRH.

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Fig. 14. Imaging results calculated with manifold matrices of 9 × 6 hypothetical targets, same targets as in Fig. 13. (a) Idealized scan-converted image. (b) B-mode image result using phased array beamforming. (c) B-mode image result using SRA. (d) B-mode image result using SRD. (e) Bmode image result using SRH.

Fig. 15. Imaging results for targets with smaller spacing, calculated with manifold matrices of 21 × 6 hypothetical targets. (a) Idealized scanconverted image. (b) B-mode image result using phased array beamforming. (c) B-mode image result using SRA. (d) B-mode image result using SRD. (e) B-mode image result using SRH.

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TABLE I. B-Mode Image SNR Comparison of Different Imaging Methods.

Fig. Fig. Fig. Fig.

13 14 15 16

Phased array

SRA

SRD

SRH

27.31 30.37 30.01 28.41

31.21 29.07 37.57 40.17

36.71 31.40 31.70 44.07

38.85 40.01 34.08 61.60

Values are reported in decibels.

D. Simulation Results With Alternative Imaging Parameters The proposed methods were further tested using transducer arrays with different parameters. First, we re-sampled the impulse responses from the FEM simulation to emulate a higher frequency ring array with parameters closer to those used in [2]. The resonant frequency of the asymmetric mode was up-shifted to 8 MHz, and the excitation signal was three cycles of a 9-MHz sinusoid. The receiving data sampling rate was increased to 33 MHz. The focal distance was fixed at 20 mm. The lateral calibration grid size was reduced to −10° to 10° with 1° increment, and the test targets were three lateral targets spaced 3° apart. We used three lateral targets in this section to focus on the lateral super-resolution ability of the proposed methods. The imaging results are shown in Fig. 17. The images are shown at the same size as previous results for

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comparison. The results show that for high frequencies normally used in catheter arrays, the proposed methods perform well enough to separate very close targets in the lateral direction. The next simulation was done using a linear phased array consisting of 45 CMUT cells (approximately 5 mm in total width). To use manifold matrices of a similar dimension as previous tests, receiving signals of every third cell of the array were used. The impulse responses, excitation signals and calibration grid points were the same as the original ring array in the previous section, and the imaging targets are three lateral targets 10° apart at z = 20 mm. The simulation results of the linear array are shown in Fig. 18. Note that SRH gives a low weight to the central point, because the weight was not correctly estimated using SRA because of the small difference in its manifold columns. The above simulations with alternative imaging array parameters show the proposed methods particularly improve lateral resolution over the delay-and-sum phasedarray method, and SRD and SRH give even better lateral resolution than SRA. E. Simulation Results With an Anechoic Cyst In this simulation, the targets are 60 points randomly selected from the 126 grid points, simulating an anechoic cyst of 2 mm radius at x = −2 mm, z = 20 mm. The

Fig. 16. Imaging results of a simulated point targets phantom, calculated with manifold matrices of 21 × 6 hypothetical targets. (a) Idealized scanconverted image. (b) B-mode image result using phased array beamforming. (c) B-mode image result using SRA. (d) B-mode image result using SRD. (e) B-mode image result using SRH.

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Fig. 17. Imaging results for three laterally spread point targets using a high-frequency ring array with fine calibration grid, calculated with manifold matrices of 21 × 6 hypothetical targets. (a) Idealized B-mode image. (b) B-mode image result using phased array beamforming. (c) B-mode image result using SRA. (d) B-mode image result using SRD. (e) B-mode image result using SRH.

Fig. 18. Imaging results for three laterally spread point targets using a 45-cell linear array, calculated with manifold matrices of 21 × 6 hypothetical targets. (a) Idealized B-mode image. (b) B-mode image result using phased array beamforming. (c) B-mode image result using SRA. (d) B-mode image result using SRD. (e) B-mode image result using SRH.

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Fig. 19. Imaging results for 60 randomly selected point targets simulating a cyst, using the original ring array, calculated with manifold matrices of 21 × 6 hypothetical targets. (a) Idealized B-mode image. (b) B-mode image result using phased array beamforming. (c) B-mode image result using SRA. (d) B-mode image result using SRD. (e) B-mode image result using SRH.

transducer array is the original ring array used in the previous subsection, and the simulation results are shown in Fig. 19. The proposed methods show much better resolution than the phased-array imaging method, and SRD and SRH provide better delineation of the cyst than SRA. F. Discussion of Results The imaging results show that the inherent side lobe of a ring or linear array results in considerable blur in a traditional phased array image using delay-and-sum, whereas the proposed imaging methods using SRD and SRH give super-resolution, especially in the lateral direction. The computational cost of the proposed method can be calculated in terms of the size of each manifold matrix using the imaging parameters (excitation frequency, sampling rate, and imaging depth). As an example, for the imaging parameters used to produce the results in Fig. 13 (the excitation frequency is 3 MHz, the sampling rate is 10MHz, and the hypothetical target grid is centered at a depth of z = 20 mm). During the manifold matrix construction process, for each point target, the echo signal received by each CMUT cell for an internally set imaging depth was recorded and convolved with the impulse responses as described in Section IV-B, making

a 650-sample trace for each channel. Then the temporal traces for 12 cells were concatenated to form an approximately 8000-element column vector for the manifold matrix. The other dimension of the manifold matrix is the number of targets, namely 126 in this case. The manifold matrix then has a dimension of 8000 × 126. Note that the temporal dimension can be further reduced by truncating the temporal column. The proposed SRA, SRD, and SRH have the same manifold matrices dimensions, but the estimation accuracy of the SRD and SRH methods improves over SRA, which means a higher resolution can potentially be obtained with the same computation complexity using the differential signals. The result also shows that the image quality improves for SRA when the number of hypothetical grid points increases, i.e., the dimensions of the manifold matrices increase. This means that the differential signal requires smaller manifold matrices to achieve the similar image resolution. Furthermore, the hybrid step can improve on both types of signals while keeping the matrix dimension low. The simulations in this work were performed with a small footprint, wide beamwidth ring array in an exemplar −20° to 20° field of view (FOV). As a future direction, the proposed technique can be extended to reduce

you et al.: super-resolution imaging using multi-electrode cmuts

the computation complexity for full imaging with a large linear array. Our focused beam approach means an improved SNR inside the focal region, and a decreased SNR outside it. This allows us to extend our proposed methods to full imaging by safely dividing the FOV into small focal regions for computation. As shown in Fig. 20(a), the full FOV can be divided into smaller chunks in axial and lateral directions in which our technique can be applied in each individual chunk. The axial chunks can be extracted by truncating the echo signals from the full imaging depth, or by dynamic focusing and truncation. The size of the axial chunk may not be smaller than the pulse length. For example, a 24 000-dimension trace can be divided into three 8000-dimension traces and computed separately, reducing one matrix dimension to 1/3. The hypothetical grids can be also divided laterally into multiple sectors to be treated individually. The size of the lateral sector can be determined by the beam width at the focal depth. Scatterers outside the sector can contribute to the echoes during the imaging process, but because of the SNR falloff of the outside regions, only a few neighboring manifold matrices are needed to be concatenated for computation. For the 3-MHz ring catheter used to generate the result shown in Fig. 13, 4 chunks are needed for a 20-mm-wide FOV at z = 20 mm. The computational complexity of qTONE was estimated as in2(out + in), where in is the number of input sensor array samples, and out is the number of hypothetical scatterers in the output image [13]. Typically, imaging a full FOV using the plane wave approach in [13] requires a manifold matrix with thousands of elements in each dimension. A tiling method was proposed by the same authors to reduce the computation complexity [37]. In the tiling method, the FOV was divided into smaller tiles, and the full matrix modeling the scatterers inside the current tile is concatenated with the rank reduced matrix modeling the region outside the tile [the tiles are illustrated in Fig. 20(b)].

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Although our methods require multiple computations over the full FOV, the nearly cubic reduction of time complexity, and the quadratic reduction in spatial complexity resulting from smaller matrices even for multiple computations can still be significant compared with the original qTONE method. Compared with the tiling method, the matrix size can still be smaller because of focusing. The reduced time and spatial complexity allowed our simulations to run on a personal computer. Again, using differential signals can further improve the estimation accuracy of individual computations, which is equivalent to reducing the necessary matrix dimension. The simulation results also show that differential-signal-based new methods may generate more false positives when the spatial sampling rate of the test phantom is close to the highest spatial sampling rate of the hypothetical target grid. The pruning step may cause false negatives, especially when the hypothetical target grid is dense and estimation error is relatively large. Using a weighted average of the values from neighboring angles may be a solution. Results with different imaging parameters show the efficacy of the proposed methods for different cases compared with the delay-and-sum approach: they provide superior resolution in high-frequency operations for miniaturized devices, offer stably better performance for different array sizes and different beamwidths, and their performance is consistent in more realistic imaging cases such as randomly distributed scatterers. V. Conclusion and Discussion In this work, we proposed a novel super-resolution imaging method that takes advantage of the differential received signal of multi-electrode CMUTs for phased ring array and linear array imaging. The proposed method uses focused transmit and beamforming in receive. Manifold

Fig. 20. Extending the proposed methods to full imaging. The proposed focused approach restricts computations in small focal regions, resulting in potential reduction of computational complexity.

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matrices of multiple steering angles were constructed, and a pruning step was added to minimize the side lobe artifact. A hybrid step was used to reduce false positives from the estimations using average and differential signals. Ultrasound imaging simulation was performed with a revised Field II program using the impulse responses from FEM simulation. Imaging simulation results showed that the unique signature of the differential received signal results in higher estimation accuracy, and thus higher resolution than the classic phased array beam forming method and using average received signals. The differential signals can potentially lower the computational cost by achieving better ability of locating the targets than the average signals with the manifold matrices of the same size. This method can be readily extended to linear arrays where the scan lines are moved across the aperture. It can also be applied to plane-wave fast imaging by constructing and solving weight vectors using only one manifold matrix and omitting the weight vector pruning step. The image quality would be traded off for higher frame rate, but the differential received signals are still expected to provide more decorrelated signature than the average received signals, providing higher estimation accuracy. The proposed methods can potentially reduce the computational complexity of full imaging by computing in multiple small focal areas of the full field of view, which may be a desirable alternative to the plane wave full imaging approach. This is the first demonstration of the use of the differential signals to achieve super-resolution imaging. The main benefit appears to be the lateral resolution, not the axial resolution. The proposed approach of using the weight factor to weigh the RF signals is a simple method of achieving super-resolution imaging while still retaining the ultrasound image appearance. Similarly, the proposed hybrid method is an initial effort to combine the benefits of super-resolution axial and super-resolution lateral results. The added frond-end interconnections in the probe is a trade-off in implementation, but leaves increased flexibility for more sophisticated imaging methods. More simulations are needed to identify the optimal operating zone of the differential signals, i.e., the maximum angles, the distances from the focal zone, and the optimal operation frequencies. Future directions also include further reduction in the manifold matrix dimensions, and more sophisticated hybrid methods. The pure simulation result is a limitation, so experimental measurement of the proposed method is the focus of future work. This work is to simply demonstrate the potential of multi-electrode CMUTs for super-resolution imaging; challenging issues such as many more scatterers, variable speed of sound, and nonlinearity must be further addressed. Acknowledgments The authors thank CMC Microsystems (Kingston, ON, Canada) for their simulation software support.

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2309 Wei You was born in Nanjing, China, in 1983. She received her B.Eng. degree in electrical engineering from the Nanjing University of Science and Technology, Nanjing, China, in 2005. She received her M.A.Sc. and Ph.D. degrees in electrical and computer engineering from the University of British Columbia (UBC), Vancouver, Canada, in 2008 and 2013, respectively. Her research focuses on the design and modeling of CMUT arrays for higher image resolution, higher transduction efficiency, and wider imaging applications.

Edmond Cretu (M’91) received the M.A.Sc. in electrical engineering from the “Politechnica” University of Bucharest, Romania, in 1989, and the Ph.D. in microsystems from the Delft University of Technology, The Netherlands, in 2003. He was researcher in the Romanian Academy and Associate Assistant in the Faculty of Electrical Engineering of the “Politehnica” University of Bucharest. From 2000 until 2005, he was with Melexis Belgium as Senior Designer and Manager for MEMS-based inertial systems for automotive applications. He has been with the University of British Columbia, Canada, since 2006, where he is at present Associate Professor in the Department of Electrical and Computer Engineering. His research interest is focused on MEMS-based microsystems design for biomedical and automotive applications, and on rapid microfabrication technologies. He has received in 2005 the “Tudor Tanasescu” (Science and Information Technology) award from the Romanian Academy, for a group of papers in the field of microsystems, co-authored with L. Rocha and R. F. Wolffenbuttel.

Robert Rohling (M’00–SM’10) received the B.A.Sc. degree in engineering physics from the University of British Columbia (UBC), the M. Eng. degree in biomedical engineering from McGill University, and the Ph.D. degree in information engineering from the University of Cambridge. He worked as the project manager of 3-D medical imaging at ALI Technologies, Vancouver, Canada from 1999 to 2000, before joining the University of British Columbia, where he is now Professor. He is the coordinator of the Biomedical Engineering Option and co-coordinator of the Mechatronics program at UBC. He is also a member of DICOM on multidimensional interchange. His current research areas include adaptive ultrasound, 3-D ultrasound, elastography, and image-guided surgery.