Comments on "Iterative procedures for reduction of blocking effects in transform image coding"

In the above-titled paper (see ibid., vol. 2, p. 91-5, Mar. 1992), R. Rosenholtz and A. Zakhor proposed an effective method for reducing blocking in transform coded images. Their method uses two projection operators and the theory of projection onto convex sets (POCS) to guarantee convergence of the iteration. One projection operator is defined from the known quantization levels used to code the transform coefficients. The other projection is based on the set of bandlimited images with a given cutoff frequency. The algorithm they actually implemented is only tenuously related to the theory of POCS. A different basis for justifying their algorithm is offered, one that provides an exact formal basis for establishing convergence and a more flexible theory for elucidating the possibilities of the algorithm.<>