A construction method of optimum integer-to-integer transform based on an error propagation model

In lossless image compression, a ladder network is commonly or widely used for integer to integer transform(integer transform), where rounding operations after multiplications cause some difference between the real and integer transform (transform error). In order to remain the error value within a small range, the ladder network coefficients should be small. We previously proposed a method of exchanging the rows of transformation matrix(row exchange method) to make the ladder network coefficients smaller. As there are many exchange patterns, a method is desired for finding best or nearly best exchange pattern efficiently. This paper proposes such a method by maximizing the absolute value of trace of a submatrix of the transformation matrix.