Summary: 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.