A New SURE Approach to Image Denoising: Interscale Orthonormal Wavelet Thresholding

By Florian Luisier, Thierry Blu, Michael A. Unser. IEEE Transactions on Image Processing, 2007

694 citations recorded by the source corpus.

This paper introduces a new approach to orthonormal wavelet image denoising. Instead of postulating a statistical model for the wavelet coefficients, we directly parametrize the denoising process as a sum of elementary nonlinear processes with unknown weights. We then minimize an estimate of the mean square error between the clean image and the denoised one. The key point is that we have at our disposal a very accurate, statistically unbiased, MSE estimate-Stein's unbiased risk estimate-that depends on the noisy image alone, not on the clean one. Like the MSE, this estimate is quadratic in the unknown weights, and its minimization amounts to solving a linear system of equations. The existence of this a priori estimate makes it unnecessary to devise a specific statistical model for the wavelet coefficients. Instead, and contrary to the custom in the literature, these coefficients are not considered random any more. We describe an interscale orthonormal wavelet thresholding algorithm based on this new approach and show its near-optimal performance-both regarding quality and CPU requirement-by comparing it with the results of three state-of-the-art nonredundant denoising algorithms on a large set of test images. An interesting fallout of this study is the development of a new, group-delay-based, parent-child prediction in a wavelet dyadic tree

Subfields: Computer Vision and Pattern Recognition, Media Technology

View Paper: https://www.semanticscholar.org/paper/9ab64c8fdfdb870692b30d943266f4294dcaabb5

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Citations in the corpus

No-Reference Image Quality Assessment in the Spatial Domain (2012, background): “Although image denoising is a well studied problem in image processing [50], [51], [52], [53], [54], blind image denoising remains relatively underexplored [54], [49].”
The SURE-LET Approach to Image Denoising (2007, background): “1Some parts of this chapter are based on our published papers [92, 93].”
Super-Resolution Without Explicit Subpixel Motion Estimation (2009, methodology): “Ideally, although one would like to automatically set these regression parameters using a method such as cross-validation [23], [24] or SURE (Stein’s unbiased risk estimator) [25], this would add significant computational complexity to the already heavy load of the proposed method.”
Monte-Carlo Sure: A Black-Box Optimization of Regularization Parameters for General Denoising Algorithms (2008, background): “There is a notable exception in the context of (orthonormal) wavelet denoisin g [17], [18] where the SURE strategy has proven to be quite powerful and has been incorporated in some stat -of-the-art algorithms [19], [20], [29]; specifically, SURE-based denoising using non-orthon ormal transforms is d”
Multiresolution Bilateral Filtering for Image Denoising (2008, neutral): “D CF [14], NEW SURE THRESHOLDING [8], BLS-GSM [4], AND THE PROPOSED METHOD FOR THE SPACE VARYING NOISE SIMULATION Fig.”
Deep Convolutional Neural Network for Inverse Problems in Imaging (2016, methodology): “ct a 512 512 image on the GPU. I. INTRODUCTION Over the past decades, iterative reconstruction methods have become the dominant approach to solving inverse problems in imaging including denoising [1]–[4], deconvolution [5], [6], and interpolation [7], [8]. Thanks to robust regularizers such as total”
Multi-Wiener SURE-LET Deconvolution (2013, positive): “Here, we adopt the LET method [51], [52], and [58], which parametrizes f(y) as a linear combination of a small number of pre-defined basic functions (or processing) f k for k = 1, 2, . . . , K ; i.e., f(y) = K k=1 a k f k (y) = [f 1 (y) f 2 (y) . . . f K (y)] F(y) ⎡ ⎢ ⎢ ⎢ ⎣ a 1 a 2 . . . a K ⎤ ⎥ ⎥…”
Image Denoising in Mixed Poisson–Gaussian Noise (2011, methodology): “Similarly to what has been proposed for SURE-based denoising [2], [3], [33], [37], we describe the denoising function as the linear expansion of thresholds (LET) defined as”
Image Denoising and Inpainting with Deep Neural Networks (2012, background): “One approach is to transfer image signals to an alternative domain where they can be more easily separated from the noise [1] [2] [3].”