High-quality Image Restoration from Partial Mixed Adaptive-Random Measurements

A novel framework to construct an efficient sensing (measurement) matrix, called mixed adaptive-random (MAR) matrix, is introduced for directly acquiring a compressed image representation. The mixed sampling (sensing) procedure hybridizes adaptive edge measurements extracted from a low-resolution image with uniform random measurements predefined for the high-resolution image to be recovered. The mixed sensing matrix seamlessly captures important information of an image, and meanwhile approximately satisfies the restricted isometry property. To recover the high-resolution image from MAR measurements, the total variation algorithm based on the compressive sensing theory is employed for solving the Lagrangian regularization problem. Both peak signal-to-noise ratio and structural similarity results demonstrate the MAR sensing framework shows much better recovery performance than the completely random sensing one. The work is particularly helpful for high-performance and lost-cost data acquisition.Comment: 16 pages, 8 figure

Video Compressive Sensing for Dynamic MRI

We present a video compressive sensing framework, termed kt-CSLDS, to accelerate the image acquisition process of dynamic magnetic resonance imaging (MRI). We are inspired by a state-of-the-art model for video compressive sensing that utilizes a linear dynamical system (LDS) to model the motion manifold. Given compressive measurements, the state sequence of an LDS can be first estimated using system identification techniques. We then reconstruct the observation matrix using a joint structured sparsity assumption. In particular, we minimize an objective function with a mixture of wavelet sparsity and joint sparsity within the observation matrix. We derive an efficient convex optimization algorithm through alternating direction method of multipliers (ADMM), and provide a theoretical guarantee for global convergence. We demonstrate the performance of our approach for video compressive sensing, in terms of reconstruction accuracy. We also investigate the impact of various sampling strategies. We apply this framework to accelerate the acquisition process of dynamic MRI and show it achieves the best reconstruction accuracy with the least computational time compared with existing algorithms in the literature.Comment: 30 pages, 9 figure

Compressive Measurement Designs for Estimating Structured Signals in Structured Clutter: A Bayesian Experimental Design Approach

This work considers an estimation task in compressive sensing, where the goal is to estimate an unknown signal from compressive measurements that are corrupted by additive pre-measurement noise (interference, or clutter) as well as post-measurement noise, in the specific setting where some (perhaps limited) prior knowledge on the signal, interference, and noise is available. The specific aim here is to devise a strategy for incorporating this prior information into the design of an appropriate compressive measurement strategy. Here, the prior information is interpreted as statistics of a prior distribution on the relevant quantities, and an approach based on Bayesian Experimental Design is proposed. Experimental results on synthetic data demonstrate that the proposed approach outperforms traditional random compressive measurement designs, which are agnostic to the prior information, as well as several other knowledge-enhanced sensing matrix designs based on more heuristic notions.Comment: 5 pages, 4 figures. Accepted for publication at The Asilomar Conference on Signals, Systems, and Computers 201

Sparse signal and image recovery from Compressive Samples

In this paper we present an introduction to Compressive Sampling (CS), an emerging model-based framework for data acquisition and signal recovery based on the premise that a signal having a sparse representation in one basis can be reconstructed from a small number of measurements collected in a second basis that is incoherent with the first. Interestingly, a random noise-like basis will suffice for the measurement process. We will overview the basic CS theory, discuss efficient methods for signal reconstruction, and highlight applications in medical imaging

How to find real-world applications for compressive sensing

The potential of compressive sensing (CS) has spurred great interest in the research community and is a fast growing area of research. However, research translating CS theory into practical hardware and demonstrating clear and significant benefits with this hardware over current, conventional imaging techniques has been limited. This article helps researchers to find those niche applications where the CS approach provides substantial gain over conventional approaches by articulating lessons learned in finding one such application; sea skimming missile detection. As a proof of concept, it is demonstrated that a simplified CS missile detection architecture and algorithm provides comparable results to the conventional imaging approach but using a smaller FPA. The primary message is that all of the excitement surrounding CS is necessary and appropriate for encouraging our creativity but we all must also take off our "rose colored glasses" and critically judge our ideas, methods and results relative to conventional imaging approaches.Comment: 10 page

Wavelet-Based Compressive Sensing for Point Scatterers

Compressive Sensing (CS) allows for the sam-pling of signals at well below the Nyquist rate but does so, usually, at the cost of the suppression of lower amplitude sig-nal components. Recent work suggests that important infor-mation essential for recognizing targets in the radar context is contained in the side-lobes as well, which are often sup-pressed by CS. In this paper we extend existing techniques and introduce new techniques both for improving the accu-racy of CS reconstructions and for improving the separa-bility of scenes reconstructed using CS. We investigate the Discrete Wavelet Transform (DWT), and show how the use of the DWT as a representation basis may improve the accu-racy of reconstruction generally. Moreover, we introduce the concept of using multiple wavelet-based reconstructions of a scene, given only a single physical observation, to derive re-constructions that surpass even the best wavelet-based CS reconstructions. Lastly, we specifically consider the effect of the wavelet-based reconstruction on classification. This is done indirectly by comparing outputs of different algo-rithms using a variety of separability measures. We show that various wavelet-based CS reconstructions are substan-tially better than conventional CS approaches at inducing (or preserving) separability, and hence may be more useful in classification applications

Nearfield Acoustic Holography using sparsity and compressive sampling principles

Regularization of the inverse problem is a complex issue when using Near-field Acoustic Holography (NAH) techniques to identify the vibrating sources. This paper shows that, for convex homogeneous plates with arbitrary boundary conditions, new regularization schemes can be developed, based on the sparsity of the normal velocity of the plate in a well-designed basis, i.e. the possibility to approximate it as a weighted sum of few elementary basis functions. In particular, these new techniques can handle discontinuities of the velocity field at the boundaries, which can be problematic with standard techniques. This comes at the cost of a higher computational complexity to solve the associated optimization problem, though it remains easily tractable with out-of-the-box software. Furthermore, this sparsity framework allows us to take advantage of the concept of Compressive Sampling: under some conditions on the sampling process (here, the design of a random array, which can be numerically and experimentally validated), it is possible to reconstruct the sparse signals with significantly less measurements (i.e., microphones) than classically required. After introducing the different concepts, this paper presents numerical and experimental results of NAH with two plate geometries, and compares the advantages and limitations of these sparsity-based techniques over standard Tikhonov regularization.Comment: Journal of the Acoustical Society of America (2012