Lipschitz exponents based signal restoration

In this work, we attempt to propose a signal restoration technique from the noise corrupted signal. The main diculty in most of the noise removal approaches is the extraction of singularities which are part of the signal from noise elements. In order to over come this problem, the propose method measures the Lipschitz exponent of the transitions to extract the noise elements. Unlike many noise removal techniques, the present method works in the non orthogonal domain. These noise elements were identied from the decaying slope of modulus maxima lines and is termed as Lipschitz exponents. The main contribution of the work is the reconstruction process. By utilizing the property of Lipschitz exponents, it is possible to reconstruct the smooth signal by non linear functioning. Statistical results are quite promising and performs better than conventional shrinkage methods in the case of high variance noise. Furthermore, in order to extract noise elements the proposed method is not limited with the selection of wavelet function for the addressed signal as well.