Reversible overlap operator for efficient lossless data compression

Abstract

An efficient lapped transform is realized using pre- and post-filters (or reversible overlap operators) that are structured of unit determinant component matrices. The pre-and post-filters are realized as a succession of planar rotational transforms and unit determinant planar scaling transforms. The planar scaling transforms can be implemented using planar shears or lifting steps. Further, the planar rotations and planar shears have an implementation as reversible / lossless operations, giving as a result, a reversible overlap operator.

Description

technical field [0001] The present invention relates generally to compression of digital media (eg, video and images) using lapped transforms. Background technique [0002] overlapping transform [0003] The lapped transform is a powerful signal processing technique used in data compression. See H.S. Malvar, "Signal Processing with Lapped Transforms", Boston, MA: Artech House Press, 1992. However, an efficient lapped transform with linear phase has not been formulated nor applied to lossless (reversible) compression of data so far. [0004] As discussed in more detail below, it is known that a lapped transform can be formulated as a pre-filter before a data transform (and its inverse transform as an inverse data transform before a post-filter). See e.g. H.S. Malvar in Proc. Picture Coding Symposium, "A pre-and post-filtering technique for the reduction of blocking effects (for reducing the pre- and post-filtering techniques of blocking effects)", Sweden, Stockholm, 1987 6...

AI Technical Summary

Problems solved by technology

However, in reality, infinite precision is impossible. For lossless data compression, the requirement is to design transformations that operate on integers or fixed-precision operations, and can only completely reconstruct data represented by integers that give transformation coefficients.

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