Two-dimensional source coding by means of subblock enumeration

A technique of lossless compression via substring enumeration (CSE) is a well-known lossless compression algorithm for a one-dimensional (1D) source. The CSE uses a probabilistic model built from the circular string of an input source for encoding the source. The CSE is applicable to two-dimensional (2D) sources such as images by dealing with a line of pixels of 2D source as a symbol of an extended alphabet. At the initial step of the CSE encoding process, we need to output number of occurrences of all symbols of the extended alphabet, so that the time complexity increases exponentially when the size of source becomes large. To reduce the time complexity, we propose a new CSE which can encode a 2D source in block-by-block instead of line-by-line. The proposed algorithm uses the flat torus of an input 2D source as a probabilistic model instead of the circular string of the source. Moreover, we prove the asymptotic optimality of the proposed algorithm for 2D general sources.