An EM algorithm for wavelet-based image restoration

By Mário A. T. Figueiredo, Robert D. Nowak. 2003

1,309 citations recorded by the source corpus.

Subfields: Biomedical Engineering, Computational Mechanics, Computer Vision and Pattern Recognition

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Citations in the corpus

Interpretable Recurrent Neural Networks Using Sequential Sparse Recovery (2016, methodology): “Many algorithms have been proposed, e.g. [17, 18], for solving the LASSO problem (16).”
A Singular Value Thresholding Algorithm for Matrix Completion (2008, methodology): “…have quite a bit of history in signal and image processing and we would like to mention the works [12, 39] for total-variation minimization, [24, 25, 31] for ℓ 1 minimization, and [5, 7, 8, 19, 20, 27, 28, 46] for some recent applications in the area of image inpainting and image restoration.”
Sparse Regularization via Convex Analysis (2017, methodology): “If γ = 0 in Proposition 15, then the algorithm reduces to the classic iterative shrinkage/thresholding algorithm (ISTA) [22], [26].”
NTIRE 2017 Challenge on Single Image Super-Resolution: Dataset and Study (2017, background): “Single image super-resolution as well as image restoration research literature spans over decades [36, 20, 4, 13, 16, 3, 15, 14, 6, 32, 54, 30, 17, 23, 12, 47, 48, 10, 21].”
A framelet-based image inpainting algorithm (2008, methodology): “It was already pointed out in [18] that the iteration for general linear inverse problem is the same as the algorithm proposed in [21], which was derived in the framework of an expectation-maximization (EM) approach to a maximum penalized likelihood solution in [28].”
A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems (2009, neutral): “One of the most popular methods for solving problem (1.3) is in the class of iterative shrinkage-thresholding algorithms (ISTA), where each iteration involves matrix-vector multiplication involving A and A T followed by a shrinkage/soft-threshold step; see, e.g., [7, 15, 10, 34, 18, 35].”
11 Projected Newton-type Methods in Machine Learning (2011, methodology): “These operators are central to forward-backward splitting methods (Combettes and Pesquet, 2009)10, as well as to methods based on surrogate optimization (Figueiredo and Nowak, 2003; Daubechies et al., 2004), separable approximation (Wright et al.”
FISTA-Net: Learning a Fast Iterative Shrinkage Thresholding Network for Inverse Problems in Imaging (2020, methodology): “fﬁcient. Frequently, regularizer Ris non-smooth, which cannot be solved straightforward. First-order iterative proximal gradient methods, such as the Iterative Shrinkage/Thresholding Algorithm (ISTA) [3]–[5], Alternating Direction Method of Multipliers (ADMM) [6] and Primal Dual Hybrid Gradient (PDH”
Spectral compressive sensing (2013, methodology): “Additional algorithms for signal recovery from CS measurements include CoSaMP [46] and iterative hard thresholding (IHT) [47, 48, 49, 50].”
Fast alternating linearization methods for minimizing the sum of two convex functions (2009, neutral): “In this section we focus on comparing the performance of our basic and fast ALMs, with and without skipping steps, against ISTA, FISTA, ADAL (Algorithm 1) and SADAL (Algorithm 2) on benchmark wavelet-based image deblurring problems from [1,18].”
CNN-Based Projected Gradient Descent for Consistent CT Image Reconstruction (2017, background): “However, in either case, they are restricted to well-behaved functionals that can be minimized via a convex routine [10]–[13].”
Sparse Modeling for Image and Vision Processing (2014, methodology): “The second approach that we consider is the `1-counterpart of the iterative hard-thresholding algorithm called “iterative softthresholding” [Nowak and Figueiredo, 2001, Figueiredo and Nowak, 2003, Starck et al., 2003, Daubechies et al., 2004].”
Augmented Lagrangian alternating direction method for matrix separation based on low-rank factorization (2014, methodology): “One type of algorithm is based on a scheme called iterative shrinkage, which has been successfully applied to 1 minimization [13,17,20,26] and to matrix completion [3,36].”
Convex Optimization for Big Data: Scalable, randomized, and parallel algorithms for big data analytics (2014, neutral): “Proximal-gradient algorithm Basic proximal-gradient scheme (ISTA) [13, 25] 1.”
Adaptive total variation image deblurring: A majorization-minimization approach (2009, methodology): “Some of these methods, including Markov random field priors [4] [5] [6] [7], wavelet-based priors/regularizers [8] [9] [10] [11] [12] [13] [14] and total variation regularization [15] [16] [17] are considered the state-of-the-art.”
An iterative thresholding algorithm for linear inverse problems with a sparsity constraint (2003, neutral): “During the ﬁnal editing of the present paper, our attention was drawn to the independent work by Figueiredo and Nowak [21, 30], who, working in the diﬀerent (ﬁnite-dimensional and stochastic) framework of Maximum Penalized Likelihood Estimation for inverting a convolution operator acting on objects…”