Scampi: a robust approximate message-passing framework for compressive imaging

International Meeting on High-Dimensional Data-Driven Science 2015

Barbier, Jean^1 ; Tramel, Eric W.^2 ; Krzakala, Florent^2

Laboratoire de Théorie des Communications, Ecole Polytechnique Fédérale de Lausanne, Faculté Informatique et Communications, CH-1015, Switzerland^1

Laboratoire de Physique Statistique CNRS UMR 8550, Université P. et M. Curie et Ecole Normale Supérieure, 24 rue Lhomond, Paris

75005, France^2

关键词: Compressive imaging;    Convex optimization methods;    Expectation;    maximizations;    Linear measurements;    Model uncertainties;    Numerical experiments;    Probabilistic approaches;    Reconstruction procedure;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/699/1/012013/pdf
DOI  :  10.1088/1742-6596/699/1/012013

来源: IOP

【 摘 要 】

Reconstruction of images from noisy linear measurements is a core problem in image processing, for which convex optimization methods based on total variation (TV) minimization have been the long-standing state-of-the-art. We present an alternative probabilistic reconstruction procedure based on approximate message-passing, Scampi, which operates in the compressive regime, where the inverse imaging problem is underdetermined. While the proposed method is related to the recently proposed GrAMPA algorithm of Borgerding, Schniter, and Rangan, we further develop the probabilistic approach to compressive imaging by introducing an expectation-maximization learning of model parameters, making the Scampi robust to model uncertainties. Additionally, our numerical experiments indicate that Scampi can provide reconstruction performance superior to both GrAMPA as well as convex approaches to TV reconstruction. Finally, through exhaustive best-case experiments, we show that in many cases the maximal performance of both Scampi and convex TV can be quite close, even though the approaches are a prori distinct. The theoretical reasons for this correspondence remain an open question. Nevertheless, the proposed algorithm remains more practical, as it requires far less parameter tuning to perform optimally.