Noiseless Codelength in Wavelet Denoising

• Published in: EURASIP journal on advances in signal processing Vol. 2010; no. 1
• Main Authors: Beheshti, Soosan, Fakhrzadeh, Azadeh, Krishnan, Sridhar
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.01.2010; Springer Nature B.V; SpringerOpen
• Subjects: Data processing; Engineering; Methods; Noise; Quantum Information Technology; Research Article; Signal,Image and Speech Processing; Spintronics; Studies; Image Denoising; Thresholding Method; Additive Noise; Minimum Mean Square Error; Mean Square Error
• ISSN: 1687-6180; 1687-6172; 1687-6180
• DOI: 10.1155/2010/641842

We propose an adaptive, data-driven thresholding method based on a recently developed idea of Minimum Noiseless Description Length (MNDL). MNDL Subspace Selection (MNDL-SS) is a novel method of selecting an optimal subspace among the competing subspaces of the transformed noisy data. Here we extend the application of MNDL-SS for thresholding purposes. The approach searches for the optimum threshold for the data coefficients in an orthonormal basis. It is shown that the optimum threshold can be extracted from the noisy coefficients themselves. While the additive noise in the available data is assumed to be independent, the main challenge in MNDL thresholding is caused by the dependence of the additive noise in the sorted coefficients. The approach provides new hard and soft thresholds. Simulation results are presented for orthonormal wavelet transforms. While the method is comparable with the existing thresholding methods and in some cases outperforms them, the main advantage of the new approach is that it provides not only the optimum threshold but also an estimate of the associated mean-square error (MSE) for that threshold simultaneously.