Sparse based image compression in wavelet domain

Sparse representation techniques have been found to provide improved results in many signaling and imaging applications. Especially in the field of image compression, this technique is able to compress the images with higher compression ratio and is also able to retrieve back the compressed image with good quality and resolution. In this paper, Wavelet and Sparse based image compression technique is presented. Using Discrete Wavelet Transform (DWT), the image to be compressed is initially decomposed into approximation and detail coefficients. The approximation coefficients are encoded directly with lossless encoding technique. In the case of detailed coefficients, their sparse representations are obtained using learned dictionary and these sparse vectors are quantized and encoded. Inverse discrete wavelet transform (IDWT) is applied with the estimated detail and approximation coefficients at the decompression stage, to retrieve back the decompressed image. They key issue of learning appropriate dictionaries for obtaining the sparse vectors is addressed in this paper. The proposed algorithm is tested on several standard test images and has been validated with popular metrics namely Peak signal to noise ratio (PSNR), Structural similarity index (SSIM) and Correlation coefficient.