Image compression based on compressed sensing theory and wavelet packet analysis

The theory of compressed sensing (or compressive sampling, CS for short) indicates if a signal is sparse or compressible in a certain transform domain, the transformed higher-dimensional signal can be projected onto a lower-dimensional space by a measurement matrix, which is uncorrelated with the transform basis, and then the signal can be accurately reconstructed by solving the convex optimization problem in accordance with a small amount of measured values. The algorithm proposed in this paper combines compressed sensing theory with wavelet packet analysis, which first decomposes the original image with the wavelet packet to make it sparse, and then retains the low-frequency coefficients in line with the optimal basis of the wavelet packet, meanwhile, makes random measurements of all the high-frequency coefficients according to the compressed sensing theory, and last restores them with the orthogonal matching pursuit (OMP) method, and does the inverse transform of the wavelet packet to reconstruct the original image, to achieve the image compression. The simulation results demonstrate this algorithm of simpleness and high efficiency, with the better reconstructed image quality, is superior to the other two image compression algorithms also based on the compressed sensing theory.