Compressive sensing for 3d data processing tasks: applications, models and algorithms

摘要: Compressive sensing (CS) is a novel sampling methodology representing paradigm shift from conventional data acquisition schemes. The theory of compressive ensures that under suitable conditions compressible signals or images can be reconstructed far fewer samples measurements than what are required by the Nyquist rate. So in literature, most works on CS concentrate one-dimensional two-dimensional data. However, besides involving more data, three-dimensional (3D) processing does have particularities require development new techniques order to make successful transitions theoretical feasibilities practical capacities. This thesis studies several issues arising applications some 3D image tasks. Two specific hyperspectral imaging and video compression where either directly unmixed recovered as whole samples. main include decoding models, preprocessing reconstruction algorithms, well encoding matrices case compression. Our investigation involves three major parts. (1) Total variation (TV) regularization plays central role models studied this thesis. To solve such we propose an efficient scheme implement classic augmented Lagrangian multiplier method study its convergence properties. resulting Matlab package TVAL3 used models. Computational results show that, thanks low per-iteration complexity, proposed algorithm capable handling realistic (2) Hyperspectral typically demands heavy computational resources due enormous amount involved. We investigate low-complexity procedures unmix, sometimes blindly, compressed obtain material signatures their abundance fractions, bypassing high-complexity task reconstructing cube itself. (3) overcome "cliff effect" suffered current coding schemes, explore framework improve scalability with respect channel multi-resolution matrix, model TV-DCT function. Extensive numerical presented, obtained experiments use not only synthetic but also real measured hardware. establish feasibility robustness, various extent, algorithms. There still remain many challenges further resolved each area, hopefully progress made will represent useful first step towards meeting these future.