Two-dimensional M-transform and its application to image processing

The authors have recently proposed a new idea of signal transformation, called M-transform, by use of pseudo-random M-sequence. As is well known, any time signal is considered to be the output of a filter whose input is white noise. This fact is sometimes called "pre-whitening". Just like this pre-whitening, M-transform method says that ally periodic time signal can be considered to be the output of a filter, called M-filter, whose input is M-sequence. And M-filter is uniquely determined according to the periodic time signal. The application of M-transform to the identification of linear control system is already shown. In this paper, M-transform is extended to two dimensional (2D) case where any 2D image carl be considered to be the output of a 2D filter (we call 2D M-filter) whose input is M-array. The 2D M-filter is shown to be uniquely determined according to the image. Some properties of 2D M-transform are investigated, and it is shown that 2D M-transform has almost similar property compared to those of one-dimensional M-transform. And some applications of 2D M-transform are shown.