Sparsity Properties of Compressive Video Sampling Generated by Coefficient Thresholding

We study the compressive sampling (CS) and its application in video encoding framework. The video input is firstly transformed into suitable domain in order to achieve sparser configuration of coefficients. Then, we apply coefficient thresholding to classify which frames to be sampled compressively or conventionally. For frames chosen to undergo compressive sampling, the coefficient vectors will be projected into smaller vectors using random measurement matrix. As CS requires two main conditions, i.e. sparsity and matrix incoherence, this research is emphasized on the enhancement of sparsity property of the input signal. It was empirically proven that the sparsity enhancement could be reached by applying motion compensation and thresholding to the non-significant coefficient count. At the decoder side, the reconstruction algorithm can employ basis pursuit or L1 minimization algorithm

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 light field photography using overcomplete dictionaries and optimized projections

Light field photography has gained a significant research interest in the last two decades; today, commercial light field cameras are widely available. Nevertheless, most existing acquisition approaches either multiplex a low-resolution light field into a single 2D sensor image or require multiple photographs to be taken for acquiring a high-resolution light field. We propose a compressive light field camera architecture that allows for higher-resolution light fields to be recovered than previously possible from a single image. The proposed architecture comprises three key components: light field atoms as a sparse representation of natural light fields, an optical design that allows for capturing optimized 2D light field projections, and robust sparse reconstruction methods to recover a 4D light field from a single coded 2D projection. In addition, we demonstrate a variety of other applications for light field atoms and sparse coding, including 4D light field compression and denoising.Natural Sciences and Engineering Research Council of Canada (NSERC postdoctoral fellowship)United States. Defense Advanced Research Projects Agency (DARPA SCENICC program)Alfred P. Sloan Foundation (Sloan Research Fellowship)United States. Defense Advanced Research Projects Agency (DARPA Young Faculty Award