Author_Institution :
IBM Almaden Res. Center, San Jose, CA, USA
Abstract :
`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
Keywords :
codes; data compression; interference suppression; matrix algebra; maximum likelihood estimation; minimisation; noise; statistical analysis; wavelet transforms; MDL denoising; basis vectors; compressible component; data sequence; ideal code length; incompressible component; information-bearing signal; minimization; minimum description length principle; normalized maximum-likelihood technique; orthonormal regression matrix; speech data; squared coefficients; wavelet transforms; Linear regression; Matrix decomposition; Maximum likelihood estimation; Minimax techniques; Noise reduction; Statistical distributions; Statistics; Stochastic processes; Vectors; Wavelet transforms;
