Reconstruction of Randomly Sampled Sparse Signals Using an Adaptive Gradient Algorithm

Sparse signals can be recovered from a reduced set of samples by using compressive sensing algorithms. In common methods the signal is recovered in the sparse domain. A method for the reconstruction of sparse signal which reconstructs the remaining missing samples/measurements is recently proposed. The available samples are fixed, while the missing samples are considered as minimization variables. Recovery of missing samples/measurements is done using an adaptive gradient-based algorithm in the time domain. A new criterion for the parameter adaptation in this algorithm, based on the gradient direction angles, is proposed. It improves the algorithm computational efficiency. A theorem for the uniqueness of the recovered signal for given set of missing samples (reconstruction variables) is presented. The case when available samples are a random subset of a uniformly or nonuniformly sampled signal is considered in this paper. A recalculation procedure is used to reconstruct the nonuniformly sampled signal. The methods are illustrated on statistical examples.Comment: 14 pages, 4 figure

On some common compressive sensing recovery algorithms and applications - Review paper

Compressive Sensing, as an emerging technique in signal processing is reviewed in this paper together with its common applications. As an alternative to the traditional signal sampling, Compressive Sensing allows a new acquisition strategy with significantly reduced number of samples needed for accurate signal reconstruction. The basic ideas and motivation behind this approach are provided in the theoretical part of the paper. The commonly used algorithms for missing data reconstruction are presented. The Compressive Sensing applications have gained significant attention leading to an intensive growth of signal processing possibilities. Hence, some of the existing practical applications assuming different types of signals in real-world scenarios are described and analyzed as well.Comment: submitted to Facta Universitatis Scientific Journal, Series: Electronics and Energetics, March 201

Measurement-Adaptive Sparse Image Sampling and Recovery

This paper presents an adaptive and intelligent sparse model for digital image sampling and recovery. In the proposed sampler, we adaptively determine the number of required samples for retrieving image based on space-frequency-gradient information content of image patches. By leveraging texture in space, sparsity locations in DCT domain, and directional decomposition of gradients, the sampler structure consists of a combination of uniform, random, and nonuniform sampling strategies. For reconstruction, we model the recovery problem as a two-state cellular automaton to iteratively restore image with scalable windows from generation to generation. We demonstrate the recovery algorithm quickly converges after a few generations for an image with arbitrary degree of texture. For a given number of measurements, extensive experiments on standard image-sets, infra-red, and mega-pixel range imaging devices show that the proposed measurement matrix considerably increases the overall recovery performance, or equivalently decreases the number of sampled pixels for a specific recovery quality compared to random sampling matrix and Gaussian linear combinations employed by the state-of-the-art compressive sensing methods. In practice, the proposed measurement-adaptive sampling/recovery framework includes various applications from intelligent compressive imaging-based acquisition devices to computer vision and graphics, and image processing technology. Simulation codes are available online for reproduction purposes

Comparison of some commonly used algorithms for sparse signal reconstruction

Due to excessive need for faster propagations of signals and necessity to reduce number of measurements and rapidly increase efficiency, new sensing theories have been proposed. Conventional sampling approaches that follow Shannon-Nyquist theorem require the sampling rate to be at least twice the maximum frequency of the signal. This has triggered scientists to examine the possibilities of creating a new path for recovering signals using much less samples and therefore speeding up the process and satisfying the need for faster realization. As a result the compressive sensing approach has emerged. This breakthrough makes signal processing and reconstruction much easier, not to mention that is has a vast variety of applications. In this paper some of the commonly used algorithms for sparse signal recovery are compared. The reconstruction accuracy, mean squared error and the execution time are compared.Comment: submitted to The 8th Mediterranean Conference on Embedded Computing - MECO'201

Compressed sensing for longitudinal MRI: An adaptive-weighted approach

Purpose: Repeated brain MRI scans are performed in many clinical scenarios, such as follow up of patients with tumors and therapy response assessment. In this paper, the authors show an approach to utilize former scans of the patient for the acceleration of repeated MRI scans. Methods: The proposed approach utilizes the possible similarity of the repeated scans in longitudinal MRI studies. Since similarity is not guaranteed, sampling and reconstruction are adjusted during acquisition to match the actual similarity between the scans. The baseline MR scan is utilized both in the sampling stage, via adaptive sampling, and in the reconstruction stage, with weighted reconstruction. In adaptive sampling, k-space sampling locations are optimized during acquisition. Weighted reconstruction uses the locations of the nonzero coefficients in the sparse domains as a prior in the recovery process. The approach was tested on 2D and 3D MRI scans of patients with brain tumors. Results: The longitudinal adaptive CS MRI (LACS-MRI) scheme provides reconstruction quality which outperforms other CS-based approaches for rapid MRI. Examples are shown on patients with brain tumors and demonstrate improved spatial resolution. Compared with data sampled at Nyquist rate, LACS-MRI exhibits Signal-to-Error Ratio (SER) of 24.8dB with undersampling factor of 16.6 in 3D MRI. Conclusions: The authors have presented a novel method for image reconstruction utilizing similarity of scans in longitudinal MRI studies, where possible. The proposed approach can play a major part and significantly reduce scanning time in many applications that consist of disease follow-up and monitoring of longitudinal changes in brain MRI

Cognitive Random Stepped Frequency Radar with Sparse Recovery

Random stepped frequency (RSF) radar, which transmits random-frequency pulses, can suppress the range ambiguity, improve convert detection, and possess excellent electronic counter-countermeasures (ECCM) ability [1]. In this paper, we apply a sparse recovery method to estimate the range and Doppler of targets. We also propose a cognitive mechanism for RSF radar to further enhance the performance of the sparse recovery method. The carrier frequencies of transmitted pulses are adaptively designed in response to the observed circumstance. We investigate the criterion to design carrier frequencies, and efficient methods are then devised. Simulation results demonstrate that the adaptive frequency-design mechanism significantly improves the performance of target reconstruction in comparison with the non-adaptive mechanism.Comment: 29 pages, 13 figure

Maximum Correntropy Adaptive Filtering Approach for Robust Compressive Sensing Reconstruction

Robust compressive sensing(CS) reconstruction has become an attractive research topic in recent years. Robust CS aims to reconstruct the sparse signals under non-Gaussian(i.e. heavy tailed) noises where traditional CS reconstruction algorithms may perform very poorly due to utilizing $l_2$ norm of the residual vector in optimization. Most of existing robust CS reconstruction algorithms are based on greedy pursuit method or convex relaxation approach. Recently, the adaptive filtering framework has been introduced to deal with the CS reconstruction, which shows desirable performance in both efficiency and reconstruction performance under Gaussian noise. In this paper, we propose an adaptive filtering based robust CS reconstruction algorithm, called $l_0$ regularized maximum correntropy criterion($l_0$-MCC) algorithm, which combines the adaptive filtering framework and maximum correntropy criterion(MCC). MCC has recently been successfully used in adaptive filtering due to its robustness to impulsive non-Gaussian noises and low computational complexity. We analyze theoretically the stability of the proposed $l_0$-MCC algorithm. A mini-batch based $l_0$-MCC(MB-$l_0$-MCC) algorithm is further developed to speed up the convergence. Comparison with existing robust CS reconstruction algorithms is conducted via simulations, showing that the proposed $l_0$-MCC and MB-$l_0$-MCC can achieve significantly better performance than other algorithms

Deep Compressed Sensing

Compressed sensing (CS) provides an elegant framework for recovering sparse signals from compressed measurements. For example, CS can exploit the structure of natural images and recover an image from only a few random measurements. CS is flexible and data efficient, but its application has been restricted by the strong assumption of sparsity and costly reconstruction process. A recent approach that combines CS with neural network generators has removed the constraint of sparsity, but reconstruction remains slow. Here we propose a novel framework that significantly improves both the performance and speed of signal recovery by jointly training a generator and the optimisation process for reconstruction via meta-learning. We explore training the measurements with different objectives, and derive a family of models based on minimising measurement errors. We show that Generative Adversarial Nets (GANs) can be viewed as a special case in this family of models. Borrowing insights from the CS perspective, we develop a novel way of improving GANs using gradient information from the discriminator.Comment: ICML 201

Convolutional Sparse Coding for Compressed Sensing CT Reconstruction

Over the past few years, dictionary learning (DL)-based methods have been successfully used in various image reconstruction problems. However, traditional DL-based computed tomography (CT) reconstruction methods are patch-based and ignore the consistency of pixels in overlapped patches. In addition, the features learned by these methods always contain shifted versions of the same features. In recent years, convolutional sparse coding (CSC) has been developed to address these problems. In this paper, inspired by several successful applications of CSC in the field of signal processing, we explore the potential of CSC in sparse-view CT reconstruction. By directly working on the whole image, without the necessity of dividing the image into overlapped patches in DL-based methods, the proposed methods can maintain more details and avoid artifacts caused by patch aggregation. With predetermined filters, an alternating scheme is developed to optimize the objective function. Extensive experiments with simulated and real CT data were performed to validate the effectiveness of the proposed methods. Qualitative and quantitative results demonstrate that the proposed methods achieve better performance than several existing state-of-the-art methods.Comment: Accepted by IEEE TM

One Network to Solve Them All --- Solving Linear Inverse Problems using Deep Projection Models

While deep learning methods have achieved state-of-the-art performance in many challenging inverse problems like image inpainting and super-resolution, they invariably involve problem-specific training of the networks. Under this approach, different problems require different networks. In scenarios where we need to solve a wide variety of problems, e.g., on a mobile camera, it is inefficient and costly to use these specially-trained networks. On the other hand, traditional methods using signal priors can be used in all linear inverse problems but often have worse performance on challenging tasks. In this work, we provide a middle ground between the two kinds of methods --- we propose a general framework to train a single deep neural network that solves arbitrary linear inverse problems. The proposed network acts as a proximal operator for an optimization algorithm and projects non-image signals onto the set of natural images defined by the decision boundary of a classifier. In our experiments, the proposed framework demonstrates superior performance over traditional methods using a wavelet sparsity prior and achieves comparable performance of specially-trained networks on tasks including compressive sensing and pixel-wise inpainting