A Non-Iterative Method for Factorization of Positive Matrix in Discrete Wavelet Transform Based Image Compression

Abstract

A non-iterative method of factorizing a 4×4 positive matrix, with the application to image compression is explained using an example. The procedure is applied to all the 4096 number of 4×4 pixel sub-blocks of a 256×256 image for compression. The proposed compression technique can be applied to the Discrete Wavelet Transform (DWT) coefficients of the test image. The 16 Pixel Intensity Values (PIV) or their DWT coefficients of a 4×4 pixels sub-block of the image can be represented by the outer product of a 4×1 column matrix and a 1×4 row matrix, with Least Mean Square Error (LMSE) criterion. Hence, instead of transmitting the 16 PIVs or their DWT coefficients, the values of the 4 elements of the column matrix and the 4 elements of the row matrix alone are transmitted resulting in a maximum compression ratio of 2 (16/4+4). The receiver can recreate the 4×4 pixels sub-block or their DWT coefficients, by calculating the outer products of 4 values of column matrix with 4 values of row matrix. In case of DWT coefficients inverse DWT is applied to recreate the pixels. This principle is extended to all the sub-blocks of the 256×256 image to compress and later reconstruct the image.