Name
Abstract | ||
|---|---|---|
We propose the notion of a sample distortion (SD) function for independent and identically distributed (i.i.d) compressive distributions to fundamentally quantify the achievable reconstruction performance of compressed sensing for certain encoder-decoder pairs at a given sampling ratio. Two lower bounds on the achievable performance and the intrinsic convexity property is derived. A zeroing procedure is then introduced to improve non convex SD functions. The SD framework is then applied to analyse compressed imaging with a multi-resolution statistical image model using both the generalized Gaussian distribution and the two-state Gaussian mixture distribution. We subsequently focus on the Gaussian encoder-Bayesian optimal approximate message passing (AMP) decoder pair, whose theoretical SD function is provided by the rigorous analysis of the AMP algorithm. Given the image statistics, analytic bandwise sample allocation for bandwise independent model is derived as a reverse water-filling scheme. Som and Schniter's turbo message passing approach is further deployed to integrate the bandwise sampling with the exploitation of the hidden Markov tree structure of wavelet coefficients. Natural image simulations confirm that with oracle image statistics, the SD function associated with the optimized sample allocation can accurately predict the possible compressed sensing gains. Finally, a general sample allocation profile based on average image statistics not only illustrates preferable performance but also makes the scheme practical. |
Year | DOI | Venue |
|---|---|---|
2013 | 10.1109/TSP.2013.2286775 | IEEE Transactions on Signal Processing |
Keywords | DocType | Volume |
independent-and-identically distributed compressive distributions,turbo codes,bandwise sampling integration,sample allocation,encoder-decoder pairs,image coding,turbo message passing approach,two-state gaussian mixture distribution,compressed sensing reconstruction performance,trees (mathematics),approximation theory,wavelet transforms,bandwise sampling,gaussian distribution,reverse water-filling scheme,natural image simulations,turbo decoding,gaussian encoder-bayesian optimal approximate message passing decoder pair,distortion,zeroing procedure,data compression,analytic bandwise sample allocation,image reconstruction,image sampling,compressed sensing,concave programming,generalized gaussian distribution,bayes methods,wavelet coefficients,general sample allocation profile,hidden markov tree structure,compressed imaging analysis,message passing,intrinsic convexity property,sampling ratio,oracle image statistics,hidden markov models,sample distortion function,multiresolution statistical image model,nonconvex sd function improvement,bandwise independent model,amp algorithm | Journal | 61 |
Issue | ISSN | Citations |
24 | 1053-587X | 1 |
PageRank | References | Authors |
0.36 | 0 | 2 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Chunli Guo | 1 | 26 | 3.82 |
| Mike E. Davies | 2 | 1664 | 120.39 |