Correction of the Haar polynomials applied for compression of graphic information (Q1603059)

The purpose of the paper is to give a theoretical justification of a method to correct a polynomial in a two-dimensional Haar system which represents an image after a nonlinear approximation. This approximation consists in nullifying Fourier-Haar coefficients that are small in absolute value. The resulting lacunary polynomial does not possess the property \(m \leq T(x) \leq M\) any more, where \(m \leq f(x) \leq M\) are bounds for the initial function. The authors estimate the measure of the set where the inequality \(m \leq T(x) \leq M\) does not hold. They consider the two-dimensional Haar system in two variants: 1) a one-scale wavelet system; 2) the direct product of two one-dimensional systems.