A course in density estimation
A course in density estimation
Optimal algorithms for approximate clustering
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
SIAM Journal on Scientific and Statistical Computing
Introduction to Linear Optimization
Introduction to Linear Optimization
Improved Fast Gauss Transform and Efficient Kernel Density Estimation
ICCV '03 Proceedings of the Ninth IEEE International Conference on Computer Vision - Volume 2
Convex Optimization
Unsupervised, Information-Theoretic, Adaptive Image Filtering for Image Restoration
IEEE Transactions on Pattern Analysis and Machine Intelligence
Regularization in Regression with Bounded Noise: A Chebyshev Center Approach
SIAM Journal on Matrix Analysis and Applications
Mean-Squared Error Estimation for Linear Systems with Block Circulant Uncertainty
SIAM Journal on Matrix Analysis and Applications
Local Adaptivity to Variable Smoothness for Exemplar-Based Image Regularization and Representation
International Journal of Computer Vision
-SVD: An Algorithm for Designing Overcomplete Dictionaries for Sparse Representation
IEEE Transactions on Signal Processing
Filtering random noise from deterministic signals via datacompression
IEEE Transactions on Signal Processing
The minimax distortion redundancy in noisy source coding
IEEE Transactions on Information Theory
Universal discrete denoising: known channel
IEEE Transactions on Information Theory
Universal denoising for the finite-input general-output channel
IEEE Transactions on Information Theory
Universal Denoising of Discrete-Time Continuous-Amplitude Signals
IEEE Transactions on Information Theory
De-noising by soft-thresholding
IEEE Transactions on Information Theory
The curvelet transform for image denoising
IEEE Transactions on Image Processing
Image denoising using scale mixtures of Gaussians in the wavelet domain
IEEE Transactions on Image Processing
Kernel Regression for Image Processing and Reconstruction
IEEE Transactions on Image Processing
Pointwise Shape-Adaptive DCT for High-Quality Denoising and Deblocking of Grayscale and Color Images
IEEE Transactions on Image Processing
Image Denoising by Sparse 3-D Transform-Domain Collaborative Filtering
IEEE Transactions on Image Processing
A universal scheme for Wyner-Ziv coding of discrete sources
IEEE Transactions on Information Theory
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We revisit the problem of denoising a discrete-time, continuous-amplitude signal corrupted by a known memoryless channel. By modifying our earlier approach to the problem, we obtain a scheme that is much more tractable than the original one and at the same time retains the universal optimality properties. The universality refers to the fact that the proposed denoiser asymptotically (with increasing block length of the data) achieves the performance of an optimum denoiser that has full knowledge of the distribution of a source generating the underlying clean sequence; the only restriction being that the distribution is stationary. The optimality, in a sense we will make precise, of the denoiser also holds in the case where the underlying clean sequence is unknown and deterministic and the only source of randomness is in the noise. The schemes involve a simple preprocessing step of quantizing the noisy symbols to generate quantized contexts. The quantized context value corresponding to each sequence component is then used to partition the unquantized symbols into subsequences. A universal symbol-by-symbol denoiser (for unquantized sequences) is then separately employed on each of the subsequences. We identify a rate at which the context length and quantization resolution should be increased so that the resulting scheme is universal. The proposed family of schemes is computationally attractive with an upper bound on complexity which is independent of the context length and the quantization resolution. Initial experimentation seems to indicate that these schemes are not only superior from a computational viewpoint, but also achieve better denoising in practice.