Rank-deficient and discrete ill-posed problems: numerical aspects of linear inversion
Rank-deficient and discrete ill-posed problems: numerical aspects of linear inversion
Digital Image Processing
Near-Optimal Parameters for Tikhonov and Other Regularization Methods
SIAM Journal on Scientific Computing
Statistical Regularization of Inverse Problems
SIAM Review
Introduction to Stochastic Search and Optimization
Introduction to Stochastic Search and Optimization
Convex Optimization
Learning from Examples as an Inverse Problem
The Journal of Machine Learning Research
Optimal Design of Experiments (Classics in Applied Mathematics) (Classics in Applied Mathematics, 50)
Deblurring Images: Matrices, Spectra, and Filtering (Fundamentals of Algorithms 3) (Fundamentals of Algorithms)
Image Processing And Analysis: Variational, Pde, Wavelet, And Stochastic Methods
Image Processing And Analysis: Variational, Pde, Wavelet, And Stochastic Methods
Stochastic Optimization: Algorithms and Applications (Applied Optimization, Volume 54) (Applied Optimization)
Robust Stochastic Approximation Approach to Stochastic Programming
SIAM Journal on Optimization
A constraint-reduced variant of Mehrotra's predictor-corrector algorithm
Computational Optimization and Applications
Wiener filter design using polynomial equations
IEEE Transactions on Signal Processing
Monte Carlo bounding techniques for determining solution quality in stochastic programs
Operations Research Letters
Experimental Design for Biological Systems
SIAM Journal on Control and Optimization
A tutorial on rank-based coefficient estimation for censored data in small- and large-scale problems
Statistics and Computing
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Spectral filtering suppresses the amplification of errors when computing solutions to ill-posed inverse problems; however, selecting good regularization parameters is often expensive. In many applications, data are available from calibration experiments. In this paper, we describe how to use such data to precompute optimal spectral filters. We formulate the problem in an empirical Bayes risk minimization framework and use efficient methods from stochastic and numerical optimization to compute optimal filters. Our formulation of the optimal filter problem is general enough to use a variety of assessments of goodness of the solution estimate, not just the mean square error. The relationship with the Wiener filter is discussed, and numerical examples from signal and image deconvolution illustrate that our proposed filters perform consistently better than well-established filtering methods. Furthermore, we show how our approach leads to easily computed uncertainty estimates for the pixel values.