The Implementation of SURE Guided Piecewise Linear Image Denoising

Yi-Qing Wang
2013 Image Processing On Line  
SURE (Stein's Unbiased Risk Estimator) guided Piecewise Linear Estimation (S-PLE) is a recently introduced patch-based state-of-the-art denoising algorithm. In this article, we focus on its implementation and show its performance by comparing it with several other acclaimed algorithms. Source Code ANSI C source code for both S-PLE and PLE is accessible on the article web page. A live demo for S-PLE can be found at the IPOL web page of this article 1 . for some integer K, positive scalars (w k )
more » ... tive scalars (w k ) 0≤k≤K−1 with K−1 k=0 w k = 1, vectors (µ k ) 0≤k≤K−1 , and positive semidefinite matrices (Σ k ) 0≤k≤K−1 representing the number of Gaussian components in the mixture, their prior probabilities, expectations, and covariance matrices. Notational convention: deterministic parameters required to be estimated for model building are written in bold. And those supposedly random quantities and absolute constants are in normal font. The observation model for image denoising under GMM is P = K−1 k=0 1 s P =k P + N with s P , the patch model selector, a discrete random variable distributed according to (w k ) 0≤k≤K−1 and independent of the noise term N . And the conditional expectation of P givenP , which constitutes the optimal filter in the L 2 sense, has a closed form which turns out to be a patch-dependent combination of K fixed linear filters. The field has known significant progress in the last few decades. DCT [26] showcases the versatility of the shrinkage [9] when combined with a good basis. BLS-GSM [17] illustrates the power of natural image statistics modeling in the wavelet domain. Non-Local Means (NLM) [3, 4] , inspired in part by the pioneering work by Efros et al. [10] in texture synthesis, effectively exploits information redundancy in natural images. Through similar patch grouping and collaborative filtering, BM3D [6, 14] further enhanced NLM and catapulted it to one of the best performing denoising methods that define the current state-of-the-art. Non-Local Bayes (NLBayes) [16] in turn improves BM3D by aggressively going after flat areas in an image and largely addresses its tendency to create artifacts in strong noise.
doi:10.5201/ipol.2013.52 fatcat:xsb6m2nfh5aeboxgrcpnd5f2hm