Compressed sensing based on the single layer wavelet transform for image processing

Abstract

According to the properties of wavelet transform sub-bands, an improved compressed sensing algorithm based on the single layer wavelet transform was proposed, which only measured the high-pass wavelet coefficients of the image but preserving the low-pass wavelet coefficients. For the reconstruction, by using the orthogonal matching pursuit (OMP) algorithm, high-pass wavelet coefficients could be recovered by the measurements. Then the image could be reconstructed by the inverse wavelet transform. Compared with the original compressed sensing algorithm, simulation results demonstrated that the proposed algorithm improved the quality of the recovered image significantly. For the same measurement number, the PSNR of the proposed algorithm was improved about 2~4 dB.