An image compression algorithm using reordered wavelet coefficients with compressive sensing

In this paper, we propose a new approach for image compression based on compressive sensing (CS). We introduce a new formulation of sparse vectors for rearranging multilevel 2-D Wavelet coefficients into a structured manner using parent-child relationships. We then use a Gaussian measurement matrix normalized with the weighted average Root Mean Squared (RMS) energies of different wavelet subbands. Compressed sampling is finally performed using this normalized measurement matrix. At the decoding stage, the image is reconstructed using a simple ℓ₁-minimization technique. The proposed wavelet-based CS compression results in performance increase compared to other conventional CS-based techniques. Our experimental results show that the proposed algorithm outperforms existing approaches over different natural images.