Efficient approximations of fixed-point direct and inverse discrete cosine transform

摘要

1. A method for compression and image display, wherein the method is performed on a computer, and comprises the steps of: scaling each coefficient in the matrix of encoded coefficients of 8 × 8, one of the factor A, factor B, factor C, factor D, factor E, factor F, factor G, a factor H, factor I, or a factor J to form the matrix of scaled coefficients,! wherein A = 1024, B = 1138, C = 1730, D = 1609, E = 1264, F = 1922, G = 1788, H = 2923, I = 2718, and J = 2528,! using repeated applications of the scaled one-dimensional transform fixed-point to convert the matrix of scaled coefficients into a matrix of transformed coefficients! right shifting transformed coefficients in the matrix of transformed coefficients to form a matrix of adjusted coefficients! wherein each adjusted coefficient in the matrix of adjusted coefficients approximates a corresponding value in a matrix of values ​​that can be generated using an ideal two-dimensional inverse discrete cosine transform ( "IDCT") to the matrix of encoded coefficients! displaying a pixel block of size 8 × 8, wherein each pixel in the pixel block size of 8 × 8 includes a pixel component value based on the adjusted coefficient in the matrix of adjusted coefficients. ! wherein the step of scaling factors in the matrix coefficients comprises the steps of: scaling coefficient at position [0,0] of the matrix of encoded coefficients by the factor A,! scaling coefficient at position [0,1] of the matrix of encoded coefficients by the factor B,! scale