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

Measure What Should be Measured: Progress and Challenges in Compressive Sensing

Is compressive sensing overrated? Or can it live up to our expectations? What will come after compressive sensing and sparsity? And what has Galileo Galilei got to do with it? Compressive sensing has taken the signal processing community by storm. A large corpus of research devoted to the theory and numerics of compressive sensing has been published in the last few years. Moreover, compressive sensing has inspired and initiated intriguing new research directions, such as matrix completion. Potential new applications emerge at a dazzling rate. Yet some important theoretical questions remain open, and seemingly obvious applications keep escaping the grip of compressive sensing. In this paper I discuss some of the recent progress in compressive sensing and point out key challenges and opportunities as the area of compressive sensing and sparse representations keeps evolving. I also attempt to assess the long-term impact of compressive sensing

Adaptive-Rate Compressive Sensing Using Side Information

We provide two novel adaptive-rate compressive sensing (CS) strategies for sparse, time-varying signals using side information. Our first method utilizes extra cross-validation measurements, and the second one exploits extra low-resolution measurements. Unlike the majority of current CS techniques, we do not assume that we know an upper bound on the number of significant coefficients that comprise the images in the video sequence. Instead, we use the side information to predict the number of significant coefficients in the signal at the next time instant. For each image in the video sequence, our techniques specify a fixed number of spatially-multiplexed CS measurements to acquire, and adjust this quantity from image to image. Our strategies are developed in the specific context of background subtraction for surveillance video, and we experimentally validate the proposed methods on real video sequences

Imaging With Nature: Compressive Imaging Using a Multiply Scattering Medium

The recent theory of compressive sensing leverages upon the structure of signals to acquire them with much fewer measurements than was previously thought necessary, and certainly well below the traditional Nyquist-Shannon sampling rate. However, most implementations developed to take advantage of this framework revolve around controlling the measurements with carefully engineered material or acquisition sequences. Instead, we use the natural randomness of wave propagation through multiply scattering media as an optimal and instantaneous compressive imaging mechanism. Waves reflected from an object are detected after propagation through a well-characterized complex medium. Each local measurement thus contains global information about the object, yielding a purely analog compressive sensing method. We experimentally demonstrate the effectiveness of the proposed approach for optical imaging by using a 300-micrometer thick layer of white paint as the compressive imaging device. Scattering media are thus promising candidates for designing efficient and compact compressive imagers.Comment: 17 pages, 8 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