Noise mitigated compressive sensing for radar applications

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.

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) is a technique that enables signal reconstruction at sub-Nyquist rate and has been widely used for fast reconstruction of multi-view video sequences (MVS) in the surveillance application. In this paper, we propose compressed-sensing recovery of MVS exploiting the model of structural group sparse representation (SGSR) along with a targeted database. SGSR groups similar patches together coupled with learning the adaptive basis from the similar groups, which gets sparser representation and thereby performs better in CS recovery. A targeted database can be easily obtained from the MVS due to their abundant prior information and the database can help us obtain more accurate similar patches, which further improve the performance with SGSR. Considering images as compressible signals rather than sparse signals, we design a filtering to retain the details of images. Simulation results show that the proposed algorithm outperforms existing reconstruction algorithms.

Compressed Sensing with Gaussian Sampling Kernel for Ultrasound Imaging

Microwave Imaging offers safe, low-cost, and portable method for medical imaging applications. These advantages make the microwave imaging convenient for early detection of tumor or cancer. The transmission method is one of the methods in microwave imaging which provides fast measurement and simple image reconstruction. However, this method requires a great number of measurements to obtain a well-reconstructed image. In order to reduce the number of measurements, this research proposes a Compressive Sensing (CS) approach for image reconstruction on microwave imaging. Compressive Sensing allows reconstruction of a signal with fewer measurements than the conventional approach. In this research, the scanning process is conducted on Computer Simulation Technology (CST) Microwave Studio software. Two dipole antennas with 3 GHz frequency are utilized as microwave transmitter and receiver. A two-layer cube phantom acts as the scanned object. Each layer has different relative permittivity which illustrates the healthy cell and abnormal cell. To meet the framework of Compressive Sensing, a weighted matrix of Discrete Radon Transform (DRT) is created as a projection matrix which delineates the data acquisition scheme in the scanning process. Discrete Cosine Transform (DCT) is selected as sparse dictionary matrix to represent the sparse basis while Basis Pursuit is selected as sparse reconstruction algorithm to reconstruct the sparse signal from measurement data. The measured $S_{21}$ data are successfully reconstructed into an image using the Compressive Sensing approach. The reconstructed image is analyzed both qualitatively and quantitatively using image quality parameters such as Structural Similarity Index (SSIM) and Mean Squared Error (MSE).

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

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.

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.

The compressive sensing (CS) framework states that a signal that has a sparse representation in a known basis may be reconstructed from samples obtained at a sub-Nyquist sampling rate. The Fourier domain is widely used in CS applications due to its inherent properties. Sparse signal recovery applications using a small number of Fourier transform coefficients have made solutions to large-scale data recovery problems, including image recovery problems, more practical. The sparse reconstruction of 2D images is performed using the sampling patterns generated by taking the general frequency characteristics of the images into account. In this work, instead of forming a general sampling pattern for infrared (IR) images, a special sampling pattern is obtained by gathering a database to extract the frequency characteristics of IR sea-surveillance images. Experimental results show that the proposed sampling pattern provides better sparse recovery results compared to the widely used patterns proposed in the literature. It is also shown that, together with a certain image dataset, the sampling pattern generated by the proposed scheme can be generalized for various image sparse recovery applications.

This paper proposes a novel radar system, namely step-frequency with compressive sampling (SFR-CS), that achieves high target range and speed resolution using significantly smaller bandwidth than traditional step-frequency radar. This bandwidth reduction is accomplished by employing compressive sampling ideas and exploiting the sparseness of targets in the range-speed space.

The long-standing analog-to-digital conversion paradigm based on Shannon/Nyquist sampling has been challenged lately, mostly in situations such as radar and communication signal processing where signal bandwidth is so large that sampling architectures constraints are simply not manageable. Compressed sensing (CS) is a new emerging signal acquisition/compression paradigm that offers a striking alternative to traditional signal acquisition. Interestingly, by merging the sampling and compression steps, CS also removes a large part of the digital architecture and might thus considerably simplify analog-to-information (A2I) conversion devices. This so-called “analog CS,” where compression occurs directly in the analog sensor readout electronics prior to analog-to-digital conversion, could thus be of great importance for applications where bandwidth is moderate, but computationally complex, and power resources are severely constrained. In our previous work (Mamaghanian, 2011), we quantified and validated the potential of digital CS systems for real-time and energy-efficient electrocardiogram compression on resource-constrained sensing platforms. In this paper, we review the state-of-the-art implementations of CS-based signal acquisition systems and perform a complete system-level analysis for each implementation to highlight their strengths and weaknesses regarding implementation complexity, performance and power consumption. Then, we introduce the spread spectrum random modulator pre-integrator (SRMPI), which is a new design and implementation of a CS-based A2I read-out system that uses spread spectrum techniques prior to random modulation in order to produce the low rate set of digital samples. Finally, we experimentally built an SRMPI prototype to compare it with state-of-the-art CS-based signal acquisition systems, focusing on critical system design parameters and constraints, and show that this new proposed architecture offers a compelling alternative, in particular for low power and computationally-constrained embedded systems.

The importance of sparse signal structures has been recognized in a plethora of applications ranging from medical imaging to group disease testing to radar technology. It has been shown in practice that various signals of interest may be (approximately) sparsely modeled, and that sparse modeling is often beneficial, or even indispensable to signal recovery. Alongside an increase in applications, a rich theory of sparse and compressible signal recovery has recently been developed under the names compressed sensing (CS) and sparse approximation (SA). This revolutionary research has demonstrated that many signals can be recovered from severely undersampled measurements by taking advantage of their inherent low-dimensional structure. More recently, an offshoot of CS and SA has been a focus of research on other low-dimensional signal structures such as matrices of low rank. Low-rank matrix recovery (LRMR) is demonstrating a rapidly growing array of important applications such as quantum state tomography, triangulation from incomplete distance measurements, recommender systems (e.g., the Netflix problem), and system identification and control. In this dissertation, we examine CS, SA, and LRMR from a theoretical perspective. We consider a variety of different measurement and signal models, both random and deterministic, and mainly ask two questions. How many measurements are necessary? How large is the recovery error? We give theoretical lower bounds for both of these questions, including oracle and minimax lower bounds for the error. However, the main emphasis of the thesis is to demonstrate the efficacy of convex optimization---in particular l1 and nuclear-norm minimization based programs---in CS, SA, and LRMR. We derive upper bounds for the number of measurements required and the error derived by convex optimization, which in many cases match the lower bounds up to constant or logarithmic factors. The majority of these results do not require the restricted isometry property (RIP), a ubiquitous condition in the literature.

this study presents an eight array ultrasonic signal phased array sparse sampling experiment system based ultrasonic phased array technology and Compressed Sensing (CS). Proposed system considers recovery ultrasonic beam signal received eight phased array elements with sparse samples captured using sub-Nyquist model in CS recovery algorithm. We have the block defect detection test in the system. The test result approximated the actual block defect position. Based on block defect detection test, We compared sparse sampling value using spectrum estimation to Compressed Sensing recovery algorithm imaging, and no focus and focus detection effect, proved the phased array experiment system based on Compressed Sensing .it can greatly improve the detection signal to noise ratio (SNR) and sensitivity. So we verify the phased array focus can improve the detection ability.

A new compressed sensing (CS) image reconstruction method is proposed for high‐resolution wideband three‐dimensional synthetic aperture radar (SAR) imaging systems. In contrast to existing CS SAR methods that employ only a forward SAR transform in pre‐ or post‐processing, the proposed method employs both forward SAR and reverse SAR (R‐SAR) transforms in each CS iteration to improve the quality of reconstructed images. This study proposes a simple and elegant truncation repair method to combat the truncation error and utilises non‐uniform fast Fourier transform to reduce the SAR and R‐SAR transform errors, thereby ensuring the convergence of the CS algorithm and improving the quality of the reconstructed images. The proposed CS SAR method is applied to microwave and millimeter wave imaging systems for non‐destructive evaluation of materials embedded in stratified media. Three different specimens under test are measured by conventional uniform sampling and by random under‐sampling with 20% or 30% spatial points of the uniform sampling. The reconstructed images show that, albeit having much less measurement points, the proposed CS method achieves better image quality and lower background artefacts than the images reconstructed from the fully‐sampled uniform measurements.