Fuzzy-wavelet-Kalman signal reconstruction

In this paper, the evolution of the discrete wavelet transform (DWT) coefficients, from a coarse subspace to a finer one, is treated in the context of fuzzy sets and systems. In other words, the quality of the synthesis operation, in the presence of degradation, is described as a fuzzy number. To this end, the α-cuts of the quality criterion are identified through interval uncertainties, within each subband. It is shown that this framework allows for an efficient description of the underlying signal. Furthermore, extensions to 2D signals, particularly, images are presented.