Compressed Sensing with Gaussian Sampling Kernel for Ultrasound Imaging

Towards practical implementation of the compressed sensing framework for multi-element synthetic transmit aperture imaging

The recently proposed compressive sensing (CS) theory provides a new solution for multiple description coding (MDC) with fine granularity, by treating each random CS measurement as a description. The performance of CS-based MDC (CS-MDC) depends on the efficacy of the CS recovery algorithm. Existing CS recovery algorithms recover the signal in a fixed space (e.g., Wavelet, DCT, and gradient spaces) for the entire duration of the signal, even though a typical multimedia signal exhibits sparsity in time/space variant spaces. To rectify this problem and develop a better CS recovery algorithm for CSMDC, we propose a learning-based framework to conduct the CS recovery in locally adaptive spaces, and carry out a case study on image MDC. A set of prior image models are learned offline from a training set to facilitate the CS recovery in local adaptive bases. Experiments show that the learning-based CS recovery algorithm can significantly improve the performance of the previous CS-MDC technique in both PSNR and visual quality.

Compressive sampling (CS), or Compressed Sensing , has generated a tremendous amount of excitement in the signal processing community. Compressive sampling, which involves non-traditional samples in the form of randomized projections, can capture most of the salient information in a signal with a relatively small number of samples, often far fewer samples than required using traditional sampling schemes. Adaptive sampling (AS), also called Active Learning , uses information gleaned from previous observations (e.g. , feedback) to focus the sampling process. Theoretical and experimental results have shown that adaptive sampling can dramatically outperform conventional (non-adaptive) sampling schemes. This paper compares the theoretical performance of compressive and adaptive sampling for regression in noisy conditions, and it is shown that for certain classes of piecewise constant signals and high SNR regimes both CS and AS are near optimal. This result is remarkable since it is the first evidence that shows that compressive sampling, which is non-adaptive, cannot be significantly outperformed by any other method (including adaptive sampling procedures), even in the presence of noise. The performance of CS schemes for signal detection is also investigated.© (2006) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

In compressive sensing (CS), a challenge is to find a space in which the signal is sparse and, hence, faithfully recoverable. Since many natural signals such as images have locally varying statistics, the sparse space varies in time/spatial domain. As such, CS recovery should be conducted in locally adaptive signal-dependent spaces to counter the fact that the CS measurements are global and irrespective of signal structures. On the contrary, existing CS reconstruction methods use a fixed set of bases (e.g., wavelets, DCT, and gradient spaces) for the entirety of a signal. To rectify this problem, we propose a new framework for model-guided adaptive recovery of compressive sensing (MARX) and show how a 2-D piecewise autoregressive model can be integrated into the MARX framework to make CS recovery adaptive to spatially varying second order statistics of an image. In addition, MARX offers a mechanism of characterizing and exploiting structured sparsities of natural images, greatly restricting the CS solution space. Simulation results over a wide range of natural images show that the proposed MARX technique can improve the reconstruction quality of existing CS methods by 2-7 dB.

Recently, Compressive Sensing (CS) has been applied to array signal processing. In theory, Direction-of-Arrival (DOA) estimation based on CS recovery can work well in correlated environments. However, a large number of sensors (i.e., linear measurements) are still needed for CS recovery. To improve on this, we propose a new CS-based DOA estimation method with a recently designed antenna structure called the Asymmetric Antenna without Phase Center (Asym-AWPC). The best reconstruction is achieved by solving the l1-norm optimization problem, which is cast as an l1-regularized least-squares program. Simulated results indicate the effectiveness of the proposed CS-based Asym-AWPC DOA estimator in a multipath environment over a recent Asym-AWPC DOA estimator but using the Multiple Signal Classification (MUSIC) rather than CS. Further improvement on the resolution can be achieved by tuning the degree of asymmetry in designing the Asym-AWPC.

Compressed sensing (CS) has been proposed as a method of breaking the seemingly inherent tradeoff between sampling rate and resolution in a variety of applications, such as ultrasound imaging. Although various studies have demonstrated the effectiveness of using CS for sub-Nyquist sampling in ultrasound imaging, a dedicated integrated circuit (IC) has not yet been presented. This work introduces a single-chip mixer-based subarray beamformer, an important component for sub-Nyquist sampling in a CS ultrasound imaging system. The beamformer chip, which performs mixing, filtering, and summation of delayed signals within a subarray, is implemented using a single operational transconductance amplifier. We evaluated the performance of the proposed mixer-based subarray beamformer circuit fabricated using a 65 nm CMOS process with 0.4 mW ch−1 power consumption from a 1.2 V supply. Measurement results indicate that the prototype chip is suitable for subarray beamforming with a 5 ns resolution digital mixing sequence. The IC presented here is the first known implementation of a mixer-based subarray beamformer for sub-Nyquist sampling in ultrasonic applications and is expected to reduce sampling data requirements by a factor of 32.

In the Compressed Sensing (CS) framework, the underdetermined system of linear equation (USLE) can have infinitely many possible solutions. However, we intend to find the sparsest possible solution, which is l0-norm minimization. However, finding an l0 norm solution out of infinitely many possible solutions is NP-hard problem that becomes non-convex optimization problem. It has been a practically proven fact that l0 norm penalty can be adequately estimated by l1 norm, which recasts a non-convex minimization problem to a convex problem. However, l1 norm non-differentiable and gradient-based minimization algorithms are not applicable, due to this very reason there is a need to approximate l1 norm by its smooth approximation. Iterative shrinkage algorithms provide an efficient method to numerically minimize l1-regularized least square optimization problem. These algorithms are required to induce sparsity in their solutions to meet the CS recovery requirement. In this research article, we have developed a novel recovery method that uses hyperbolic tangent function to recover undersampled signal/images in CS framework. In our work, l1 norm and soft thresholding are both approximated with the hyperbolic tangent functions. We have also proposed the criteria to tune optimization parameters to get optimal results. The error bounds for the proposed l1 norm approximation are evaluated. To evaluate performance of our proposed method, we have utilized a dataset comprised of 1-D sparse signal, compressively sampled MR image and cardiac cine MRI. The MRI is an important imaging modality for assessing cardiac vascular function. It provides the ejection fraction and cardiac output of the heart. However, this advantage comes at the cost of a slow acquisition process. Hence, it is essential to speed up the acquisition process to take the full benefits of cardiac cine MRI. Numerical results based on performance metrics, such as Structural Similarity (SSIM), Peak Signal to Noise Ratio (PSNR) and Root Mean Square Error (RMSE) show that the proposed tangent hyperbolic based CS recovery offers a much better performance as compared to the traditional Iterative Soft Thresholding (IST) recovery methods.

During decades microwave imaging technology has achieved remarkable progress, and at the same time encountered increasing complexity in system implementation. Recently, the sparse systems, where the compressed sensing (CS) is applied, introduce the sparse signal processing theory to radar imaging to obtain a new system methodology of microwave imaging and facilitate the burden of computing large-scale data. Basically, CS recovery is a kind of sparse regularized optimization, where the regularization parameter λ plays an important role for a stable solution. Although there are a lots of methods to estimate λ, e.g. the L-curve method, the cross-validation method, etc., however, they are still complex and even only work for particular conditions. In this paper, we will introduce a novel approach, named noise mitigated method (NMM), to get a stable result even without a precise estimation of λ. For radar applications we will take the stepped frequency radar (SFR) as an example to present the feasibility of NMM.

Compressed Sensing (CS) exploits sparsity of images to reconstruct them exactly from a small set of measurements. Recent studies have shown that nonlocal sparsity leads to superior results in CS recovery. In this paper, we first propose a new sparsity model, which is characterized as a function of the coefficients achieved by transforming the 3D array generated from a set of similar image patches. The function which we use is the nonconvex Garrote function. To efficiently solve the proposed corresponding optimization problem, we then employ an accelerated algorithm based on iterative proximal methods. Our reconstruction method exploits the benefits of both nonlocal sparsity and nonconvex optimization. Experimental results show effectiveness of the proposed method compared with the many existing algorithms in CS image recovery.

Uterine positional changes can reduce the accuracy of radiotherapy for cervical cancer patients. The purpose of this study was to; 1) Quantify the inter-fractional uterine displacement using a novel 3D ultrasound (US) imaging system, and 2) Compare the result with the bone match shift determined by Cone- Beam CT (CBCT) imaging.Five cervical cancer patients were enrolled in the study. Three of them underwent weekly CBCT imaging prior to treatment and bone match shift was applied. After treatment delivery they underwent a weekly US scan. The transabdominal scans were conducted using a Clarity US system (Clarity® Model 310C00). Uterine positional shifts based on soft-tissue match using US was performed and compared to bone match shifts for the three directions. Mean value (±1 SD) of the US shifts were (mm); anterior-posterior (A/P): (3.8±5.5), superior-inferior (S/I) (-3.5±5.2), and left-right (L/R): (0.4±4.9). The variations were larger than the CBCT shifts. The largest inter-fractional displacement was from -2 mm to +14 mm in the AP-direction for patient 3. Thus, CBCT bone matching underestimates the uterine positional displacement due to neglecting internal uterine positional change to the bone structures. Since the US images were significantly better than the CBCT images in terms of soft-tissue visualization, the US system can provide an optional image-guided radiation therapy (IGRT) system. US imaging might be a better IGRT system than CBCT, despite difficulty in capturing the entire uterus. Uterine shifts based on US imaging contains relative uterus-bone displacement, which is not taken into consideration using CBCT bone match.

Editorial

This paper introduces a compressive sampling (CS) scheme for pulse stream images. We adopt a particular sparse sampling matrix, that we call Radon-like CS matrix. Whilst the Radon transform evaluates projections of a given image along different directions, the Radon-like CS matrix evaluates randomly weighted projections of the image along a few directions. We demonstrate that the such CS measurements are invertible and assess the reconstruction accuracy of CS with the Radonlike sampling matrix by numerical trials. The Radon-like CS performs almost as well as state of the art techniques, with a reduced number of operations. As an application example, we show that, when implemented in a resource limited framework such as a Smart Sensors Grid, the sampling matrix significantly reduces inter-node signaling and then the associated energy consumption. © 2012 IEEE.

The purpose of this study was to compare between compressed sensing (CS) and deep learning (DL) accelerated T1ρ mapping in knee cartilage, a quantitative imaging technique that provides valuable information for disease diagnosis but requires long scan time. Both retrospectively and prospectively undersampled reconstruction were evaluated in nine volunteers including three with diagnosed pathology. For data collection, DESS images were collected for segmentation of six cartilage compartments. T1ρ-weighted 3D MAPSS sequence was used to create T1ρ maps. A 3T MRI scanner was used and GRAPPA 2 accelerated data were collected to provide 8-echo reference T1ρ maps and was retrospectively undersampled for reconstruction with two sampling schemes: 4 TSLs with each echo image undersampled by 4 (UF4_4echo), and 8 TSLs with each echo image undersampled by 8 (UF8_8echo). Separate prospectively undersampled datasets were also collected for reconstruction. Volunteers were scanned and rescanned with repositioning for repeatability comparison. Reference, retrospectively undersampled reconstruction, and prospectively undersampled reconstruction were compared by voxel-wise median normalized absolute differences (MNADs), concordance correlation coefficient (CCC), and coefficient of variation (CV) using cartilage compartment-wise mean value. As a result, for retrospective undersampling, CS showed CCC 0.992, MNAD 10.0%, and CV 1.3% for UF4_4echo, and CCC 0.988, MNAD 9.9%, and CV 1.4% for UF8_8echo. DL showed CCC 0.971, MNAD 9.8%, and CV 1.7% for UF4_4echo, and CCC 0.968, MNAD 10.6%, and CV 1.7% for UF8_8echo. For prospective undersampling, CS showed CCC 0.853 and CV 3.3% for UF4_4echo, and CCC 0.754 and CV 3.9% for UF8_8echo. DL showed CCC 0.939 and CV 2.4% for UF4_4echo and CCC 0.845 and CV 2.8% for UF8_8echo. The maps had 2.57%, 3.80%, 2.79%, 2.29%, and 2.85% scan-rescan CV, respectively, for reference, CS UF4_4echo, CS UF8_8echo, DL UF4_4echo, and DL UF8_8echo reconstructions. As a conclusion, DL provided better results compared to CS in prospectively undersampled reconstruction.

Multiphase flow measurements, based on tomographic imaging techniques, have made substantial progress in the past several years. In particular, ultrasonic tomographic reconstruction has shown its high potential in accurately measuring fluid fractions in a flow cross-section based on direct flow measurements. These types of measurements are very attractive as the system is nonradioactive, has direct contact to fluid, yet without flow obstruction. An ultrasonic tomographic multiphase flow meter (UTM) is being developed to capture the fluid flow rates and phase compositions in producing oil wells. The UTM aims to generate cross-sectional images of the flow inside the pipe. To recover these images, complex computations and high processing time are required, based on a limited amount of available data. For this purpose, compressive sensing (CS) reconstruction methods have shown great potential in overcoming the mentioned data quality and quantity issues. CS builds upon the fact that one can recover certain data of interest from potentially very few measurements. Many CS algorithms have been proposed in the literature. In this paper, we seek to find a suitable algorithm by comparing different CS algorithms in terms of the resulting recovered image quality. Specifically, we survey three algorithms in CS, namely basis pursuit, iterative soft thresholding (IST), and orthogonal matching pursuit (OMP). We also compare the results of the CS algorithms to that of a least-square based conventional algorithm. The numerical results show the superiority of CS recovery algorithms over the conventional approach, both qualitatively and quantitatively. The results also suggest that high image quality could potentially be achieved with less complex CS algorithms, i.e., the IST and OMP algorithms. As presented in the paper, our goal is to adapt CS reconstruction algorithms for images generated by the UTM, for the purpose of accurate quantification of oil, gas, and water phase fractions produced from different wells.

Compressive sensing (CS) theory proves that signals can be recovered from far fewer random measurements than that suggested by Nyquist-Shannon theorem. This advantage of CS is extremely useful in some data processing applications, especially in video processing. Considering that nonlocal patch-based CS methodology has achieved an impressive performance in image CS field, it motivates us to generalize the idea into the video CS filed. In this paper, by taking account of the spatiotemporal information, we propose a novel strategy to reconstruct the non-key frames of a video sequence by introducing the nonlocal similar patch group from some key frames. Experimental results illustrate that our proposed nonlocal patch-based video CS recovery algorithm can extremely exploit the information of the key frames, and achieve a better performance compared with some existing popular video CS recovery algorithms. It is noted that our idea to construct a spatiotemporal comprehensive patch group may be combined with any nonlocal patch-based CS method for video reconstruction, which leads to various of nonlocal patch-based compressive sensing video recovery algorithms.