Investigations of Image Compression using Polynomial Fitting of the Singular Values

An image, though it appears simple, needs numerous pixel values to represent it. If the image may be represented using lesser number of parameters, the image may be easily processed, stored, and transmitted. There are several techniques for compression. For example, singular value decomposition (SVD), Eigen values based analysis, discrete cosine transform, wavelet based transform, etc. Although each of these techniques has been used extensively in literature, SVD has been shown more advantageous. In the present research, the variation of singular values is approximated by a polynomial and at the time of synthesis, singular values are computed from the polynomial whose coefficients are estimated at the time of analysis. The objective is to explore the use of polynomial fitting for representing the whole set of singular values. Because the polynomial equation may be represented using smaller number of coefficients, it may be expected that the proposed technique would reduce the size of the image leading to better compression ratio.