Associations between MSE and SSIM as cost functions in linear decomposition with application to bit allocation for sparse coding

The traditional image quality assessments, such as the mean squared error (MSE), the signal-to-noise ratio (SNR), and the Peak signal-to-noise ratio (PSNR), are all based on the absolute error of images. Structural similarity (SSIM) index is another important image quality assessment which has been shown to be more effective in the human vision system (HVS). Although there are many essential differences between MSE and SSIM, some important associations exist between them. In this paper, the associations between MSE and SSIM as cost functions in linear decomposition are investigated. Based on the associations, a bit-allocation algorithm for sparse coding is proposed by considering both the reconstructed image quality and the reconstructed image contrast. In the proposed algorithm, the space occupied by a linear coefficient of a basis in sparse coding is reduced to only 9 to 10 bits, in which 1 bit is used to save the sign of linear coefficient, 3 bits are used to save the number of powers of 10 in scientific notation, and only 5 to 6 bits are used to save the significance digits. The experimental results show that the proposed bit-allocation algorithm for sparse coding can maintain both the image quality and the image contrast well.