Analysis of Sensing Matrix Design for Under-Sampling MRI

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

The sparse representation error (SRE) exists when the images are represented sparsely. The SRE is particularly large in unmanned aerial vehicles (UAV) images due to the disturbance of the harsh environment or the instability of its flight, which will bring more noise. In the compressed sensing (CS) system, the projected SRE in the compressed measurement will bring a significant challenge to the recovery accuracy of the images. In this work, a new SRE structure is proposed. Following the new structure, a lower sparse representation error (LSRE) is achieved by eliminating groups of sparse representation. With the proposed LSRE modeling, a robust sensing matrix is designed to compress and encrypt the UAV images. Experiments for UAV images are carried out to compare the recovery performance of the proposed algorithm with the existing related algorithms. The results of the proposed algorithm reveal superior recovery accuracy. The new CS framework with the proposed sensing matrix to address the scenario of UAV images with large SRE is dominant.

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.

Electrical capacitance volume tomography is a volumetric tomography technique that utilizes capacitance and fringing to capture behavior or perturbation in the sensing domain. One of the crucial issues in developing ECVT technology is the reconstruction algorithm. In practice, ILBP is most used due to its simplicity. However, it still presents elongation errors for certain dielectric contrasts. The high undersampling measurement of the ECVT imaging system, which is mathematically defined as an undetermined linear system, is one of the most challenging issues. Compressive sensing (CS) is a framework that enables the recovery of a sparse signal or a signal that can be represented as sparse in a certain domain, by having a lower dimension of measurement data compared to the Shanon-Nyquist theorem. Thus, mathematically, this framework is promising for solving an undetermined linear system such as the ECVT imaging system. This paper discusses the possibility of developing an ECVT imaging technique for static objects based on a CS framework. Based on the simulation results, Non-optimized CS does not completely succeed in providing better ECVT imaging quality. However, it does provide more localized imaging compared to ILBP. In addition, by having fewer requirements for the measurement data dimension, the CS framework is promising for reducing the number of required electrodes.

A review of the most recent contributions in the framework of Compressive Sensing (CS) strategies as applied to Electromagnetics is presented in this work. Towards this end, the CS fundamentals are firstly discussed in the light of their impact in Electromagnetics technologies. A set of CS applicative scenarios is then discussed, taking into account problems coming from antenna array design and diagnosis, direction-of-arrival estimation, and microwave imaging. An assessment of the effectiveness and potentialities of CS techniques in Electromagnetics is provided by selected numerical examples.

Compressed wide spectrum sensing scheme based on BP network

Compressive sensing (CS) idea enables the reconstruction of a sparse signal from a small set of measurements. CS approach has applications in many practical areas. One of the areas is radar systems. In this article, the radar ambiguity function is denoised within the CS framework. A new denoising method on the projection onto the epigraph set of the convex function is also developed for this purpose. This approach is compared to the other CS reconstruction algorithms. Experimental results are presented1.

Compressive sensing (CS) is a signal processing technique that enables a signal that has a sparse representation in a known basis to be reconstructed using measurements obtained below the Nyquist rate. Single detector image reconstruction applications using CS have been shown to give promising results. In this study, we investigate the application of CS theory to single detector infrared (IR) rosette scanning systems which suffer from low performance compared to costly focal plane array (FPA) detectors. The single detector pseudoimaging rosette scanning system scans the scene with a specific pattern and performs processing to estimate the target location without forming an image. In this context, this generation of scanning systems may be improved by utilizing the samples obtained by the rosette scanning pattern in conjunction with the CS framework. For this purpose, we consider surface-to-air engagement scenarios using IR images containing aerial targets and flares. The IR images have been reconstructed from samples obtained with the rosette scanning pattern and other baseline sampling strategies. It has been shown that the proposed scheme exhibits good reconstruction performance and a large size FPA imaging performance can be achieved using a single IR detector with a rosette scanning pattern.

Multipath exploitation for through-wall radar imaging (TWRI) under the framework of compressive sensing (CS) is a promising method to obtain a high-resolution image with limited number of measurements. The capability of the existing method is limited due to the model error caused by approximated dictionary matrix calculated using ray optics method. In this paper, multipath propagation is calculated by finite-difference time domain (FDTD) technique and then compensated to obtain the linear inverse model correctly. Afterwards, sparse reconstruction is used to solve this linear inverse problem. Numerical results demonstrate that the proposed approach yields high resolution image free of multipath ghosts, thus allowing to increase the signal-to-clutter ratio image.

A compressive sensing (CS) based approach is applied in conjunction with an adaptive basis re-weighting procedure for multi-dimensional stochastic process power spectrum estimation. In particular, the problem of sampling gaps in stochastic process records, occurring for reasons such as sensor failures, data corruption, and bandwidth limitations, is addressed. Specifically, due to the fact that many stochastic process records such as wind, sea wave and earthquake excitations can be represented with relative sparsity in the frequency domain, a CS framework can be applied for power spectrum estimation. By relying on signal sparsity, and the assumption that multiple records are available upon which to produce a spectral estimate, it has been shown that a re-weighted CS approach succeeds in estimating power spectra with satisfactory accuracy. Of key importance in this paper is the extension from one-dimensional vector processes to a broader class of problems involving multidimensional stochastic fields. Numerical examples demonstrate the effectiveness of the approach when records are subjected to up to 75% missing data.

Computed Tomography (CT) is one of the significant research areas in medical image analysis. One of the main aspects of CT that researchers remain focused, is on reducing the dosage as X-rays are generally harmful to human bodies. In order to reduce radiation dosage, compressed sensing (CS) based methodologies appear to be promising. The basic premise is that medical images have inherent sparsity in some transformation domain. As a result, CS provides the possibility of recovering a high quality image from fewer projection data. In general, the sensing matrix in CT is generated from Radon projections by appropriately sampling the radial and angular parameters. In our work, by restricting the number of such parameters, we generate an under-determined linear system involving projection (Radon) data and a sparse sensing matrix, bringing thereby the problem into CS framework.

Single image super-resolution based on compressive sensing and improved TV minimization sparse recovery

The estimation of ocean acoustic sound speed profiles (SSPs) requires the inversion of an acoustic transmission model using limited observations. Provided the parameters of the inverse model are sparse, Compressive Sensing (CS) can help solve such underdetermined problems accurately, efficiently, and with enhanced resolution. Here, CS is used to estimate range-independent acoustic SSPs in shallow water ocean environments using a normal-mode representation of the acoustic field. Two sparse parameterizations of the SSPs are considered. The first parameterization assumes that change in the sound speed with depth is sparse and that the SSP can be constructed from a limited number of dominant changes in sound speed. The second case assumes a priori information about the ocean SSP variability in terms of Empirical Orthogonal Functions (EOFs), estimating the dominant EOFs describing the current SSP. For both cases, both real and synthetic acoustic data are processed. It is shown that in the CS framework, both of the optimizations can be solved with increased resolution and robustness over traditional methods.

Hyperspectral imaging has a wide range of applications; however, due to the high dimensionality of the data involved, the complexity and cost of hyperspectral imagers can be prohibitive. Exploiting redundancies along the spatial and spectral dimensions of a hyperspectral image of a scene has created new paradigms that do away with the limitations of traditional imaging systems. While Compressive Sensing (CS) approaches have been proposed and simulated with success on already acquired hyperspectral imagery, most of the existing work relies on the capability to simultaneously measure the spatial and spectral dimensions of the hyperspectral cube. Most real-life devices, however, are limited to sampling one or two dimensions at a time, which renders a significant portion of the existing work unfeasible. In this paper we propose a novel CS framework that is a hybrid between traditional vectorized approaches and recently proposed tensorial approaches, and that is compatible with real-life devices both in terms of the acquisition and reconstruction requirements.

Compressive sensing (CS) techniques have been shown to enhance the performance of sparse channel estimation. This paper addresses CS-based sparse channel estimation in practical systems where the measurements are quantized to a finite number of bits. In these systems, quantization introduces two kinds of errors into the CS framework: quantization errors and saturation errors. To combat the effect of quantization error on estimating the sparse channel, a new complex-valued cost function is formulated based on the quantization model. To minimize this cost function, a multi-bit iterative hard thresholding algorithm is proposed. The channel estimate performance is evaluated by modeling the quantization error as white Gaussian noise. Our simulation results quantify the number of bits needed for our proposed quantized CS-based sparse channel estimate to achieve satisfactory performance.