MDL Denoising

The so-called denoising problem, relative to normal models for noise, is formalized such that`noise' is deened as the incompressible part in the data while the compressible part deenes the meaningful information bearing signal. Such a decomposition is eeected by minimization of the ideal code length, called for by the Minimum Description Length (MDL) principle, and obtained by an application of the normalized maximum likelihood technique to the primary parameters, their range, and their number. For any orthonormal regression matrix, such as deened by wavelet transforms, the minimization can be done with a threshold for the squared coeecients resulting from the expansion of the data sequence in the basis vectors deened by the matrix.