COMPRESSED SENSING BY ITERATIVE THRESHOLDING OF GEOMETRIC WAVELETS: A COMPARING STUDY

Abstract

Recently, a new compressed-sensing (CS) theory for simultaneous sampling and compression of signals has been applied for imaging and remote sensing. The CS makes it possible for us to take super-resolution photos only using one or a few pixels rather than millions of pixels by conventional digital cameras. However, the performances of CS are related to choices of a measurement matrix and a sparse transform. In this paper, we present an experimentally comparing study for the use of different measurement matrices (e.g., random matrices, noiselet transform matrices, and scrambled block Hadamard ensemble) in encoding step and different geometric wavelets (e.g., curvelets and bandlets) in decoding step. Numerical experiments for single-pixel imaging and Fourier-domain multiple-pixel imaging indicate how to choose a suitable CS strategy to reduce the number of measurements and decoding costs.