Block compressed sensing of images using directional transforms

• Published in: 2009 16th IEEE International Conference on Image Processing (ICIP) pp. 3021 - 3024
• Main Authors: Sungkwang Mun, Fowler, J.E.
• Format: Conference Proceeding
• Language: English
• Published: IEEE 01.11.2009
• Subjects: bivariate shrinkage; Compressed sensing; contourlets; Discrete wavelet transforms; dual-tree discrete wavelet transform; Image coding; Image reconstruction; Image sampling; Matching pursuit algorithms; Signal sampling; Smoothing methods; Sparse matrices; Wavelet transforms
• ISBN: 9781424456536; 1424456533
• ISSN: 1522-4880
• DOI: 10.1109/ICIP.2009.5414429

Block-based random image sampling is coupled with a projection-driven compressed-sensing recovery that encourages sparsity in the domain of directional transforms simultaneously with a smooth reconstructed image. Both contourlets as well as complex-valued dual-tree wavelets are considered for their highly directional representation, while bivariate shrinkage is adapted to their multiscale decomposition structure to provide the requisite sparsity constraint. Smoothing is achieved via a Wiener filter incorporated into iterative projected Landweber compressed-sensing recovery, yielding fast reconstruction. The proposed approach yields images with quality that matches or exceeds that produced by a popular, yet computationally expensive, technique which minimizes total variation. Additionally, reconstruction quality is substantially superior to that from several prominent pursuits-based algorithms that do not include any smoothing.