Binary pseudowavelets and applications to bilevel image processing

This paper shows the existence of binary pseudowavelets, bases on the binary domain that exhibit some of the properties of wavelets, such as multiresolution reconstruction and compact support. The binary pseudowavelets are defined on Bⁿ (binary vectors of length n) and are operated upon with the binary operators logical and, and exclusive or. The forward transform, or analysis, is the decomposition of a binary vector into its constituent binary pseudowavelets. Binary pseudowavelets allow multiresolution, progressive reconstruction of binary vectors by using progressively more coefficients in the inverse transform. Binary pseudowavelets bases, being sparse matrices, also provide for fast transforms; moreover pseudowavelets rely on hardware-friendly operations for efficient software and hardware implementation