Solving Inverse Problems with Piecewise Linear Estimators: From Gaussian Mixture Models to Structured Sparsity

A general framework for solving image inverse problems is introduced in this paper. The approach is based on Gaussian mixture models, estimated via a computationally efficient MAP-EM algorithm. A dual mathematical interpretation of the proposed framework with structured sparse estimation is described, which shows that the resulting piecewise linear estimate stabilizes the estimation when compared to traditional sparse inverse problem techniques. This interpretation also suggests an effective dictionary motivated initialization for the MAP-EM algorithm. We demonstrate that in a number of image inverse problems, including inpainting, zooming, and deblurring, the same algorithm produces either equal, often significantly better, or very small margin worse results than the best published ones, at a lower computational cost.Comment: 30 page

Design of a digital compression technique for shuttle television

The determination of the performance and hardware complexity of data compression algorithms applicable to color television signals, were studied to assess the feasibility of digital compression techniques for shuttle communications applications. For return link communications, it is shown that a nonadaptive two dimensional DPCM technique compresses the bandwidth of field-sequential color TV to about 13 MBPS and requires less than 60 watts of secondary power. For forward link communications, a facsimile coding technique is recommended which provides high resolution slow scan television on a 144 KBPS channel. The onboard decoder requires about 19 watts of secondary power