This paper proposes a multiscale deployment of Compressed Sensing(CS) in a new transform domain for image reconstruction. The new transform, directly built in the discrete framework, combines the traditional discrete wavelet transform with shearing filter banks defined in the Pseudo-Polar frequency domain to perform multiresolution and multidirectional analysis of images. Then a specific decimation way is applied to further get rid of extra redundancy with no aliasing. The proposed transform named wavelet-based discrete shearlet transform (WBDST) which can be seen as a extension of the original discrete shearlet transform is also optimally efficient in representing images containing edges while offering a dramatically low redundant property. Furthermore, we deploy a multiscale CS scheme in WBDST domain for image reconstruction, different scales are segregated and CS is applied separately to each one. Numerical experiments demonstrate that this deployment gives much better quality reconstructions than those of the WBDST based best N-term approximation as well as the curvelets based multiscale CS scheme.

Date Published: 11 September 2013
PDF: 10 pages
Proc. SPIE 8907, International Symposium on Photoelectronic Detection and Imaging 2013: Infrared Imaging and Applications, 890740 (11 September 2013); doi: 10.1117/12.2034497

Published in SPIE Proceedings Vol. 8907:
International Symposium on Photoelectronic Detection and Imaging 2013: Infrared Imaging and Applications
Haimei Gong; Zelin Shi; Qian Chen; Jin Lu, Editor(s)