A new wavelet based efficient image compression algorithm using compressive sensing

We propose a new algorithm for image compression based on compressive sensing (CS). The algorithm starts with a traditional multilevel 2-D Wavelet decomposition, which provides a compact representation of image pixels. We then introduce a new approach for rearranging the wavelet coefficients into a structured manner to formulate sparse vectors. We use a Gaussian random measurement matrix normalized with the weighted average Root Mean Squared energies of different wavelet subbands. Compressed sampling is finally performed using this normalized measurement matrix. At the decoding end, the image is reconstructed using a simple ℓ₁-minimization technique. The proposed wavelet-based CS reconstruction, with the normalized measurement matrix, results in performance increase compared to other conventional CS-based techniques. The proposed approach introduces a completely new framework for using CS in the wavelet domain. The technique was tested on different natural images. We show that the proposed technique outperforms most existing CS-based compression methods.