A Theory for Multiresolution Signal Decomposition: The Wavelet Representation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Ten lectures on wavelets
Removing Noise and Preserving Details with Relaxed Median Filters
Journal of Mathematical Imaging and Vision
A new information-theoretic approach to signal denoising and best basis selection
IEEE Transactions on Signal Processing - Part I
Minimax threshold for denoising complex signals with Waveshrink
IEEE Transactions on Signal Processing
Optimal weighted median filtering under structural constraints
IEEE Transactions on Signal Processing
On denoising and best signal representation
IEEE Transactions on Information Theory
Adaptive wavelet thresholding for image denoising and compression
IEEE Transactions on Image Processing
A New SURE Approach to Image Denoising: Interscale Orthonormal Wavelet Thresholding
IEEE Transactions on Image Processing
Multiresolution Bilateral Filtering for Image Denoising
IEEE Transactions on Image Processing
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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.