MDL denoising

The so-called denoising problem, relative to normal models for noise, is formalized such that 'noise' is defined as the incompressible part in the data while the compressible part defines the meaningful information-bearing signal. Such a decomposition is effected 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 defined by wavelet transforms, the minimization can be done with a threshold for the squared coefficients resulting from the expansion of the data sequence in the basis vectors defined by the matrix.