On robust estimation of the location parameter

Thank you for downloading regularization of inverse problems. Maybe you have knowledge that, people have search hundreds times for their favorite novels like this regularization of inverse problems, but end up in malicious downloads. Rather than reading a good book with a cup of tea in the afternoon, instead they juggled with some infectious bugs inside their computer. regularization of inverse problems is available in our book collection an online access to it is set as public so you can download it instantly. Our book servers spans in multiple locations, allowing you to get the most less latency time to download any of our books like this one. Kindly say, the regularization of inverse problems is universally compatible with any devices to read.

Regularization Of Inverse Problems

Lectures on Cauchy’s Problem in Linear Partial Differential Equations. By J. Hadamard. Pp. viii+316. 15s.net. 1923. (Per Oxford University Press.)

Super-resolution reconstruction proposes a fusion of several low-quality images into one higher quality result with better optical resolution. Classic super-resolution techniques strongly rely on the availability of accurate motion estimation for this fusion task. When the motion is estimated inaccurately, as often happens for nonglobal motion fields, annoying artifacts appear in the super-resolved outcome. Encouraged by recent developments on the video denoising problem, where state-of-the-art algorithms are formed with no explicit motion estimation, we seek a super-resolution algorithm of similar nature that will allow processing sequences with general motion patterns. In this paper, we base our solution on the Nonlocal-Means (NLM) algorithm. We show how this denoising method is generalized to become a relatively simple super-resolution algorithm with no explicit motion estimation. Results on several test movies show that the proposed method is very successful in providing super-resolution on general sequences.

Generalizing the Nonlocal-Means to Super-Resolution Reconstruction

Linear Regression Analysis

Lanczos-hybrid regularization methods have been proposed as effective approaches for solving largescale ill-posed inverse problems. Lanczos methods restrict the solution to lie in a Krylov subspace, but they are hindered by semi-convergence behavior, in that the quality of the solution first increases and then decreases. Hybrid methods apply a standard regularization technique, such as Tikhonov regularization, to the projected problem at each iteration. Thus, regularization in hybrid methods is achieved both by Krylov filtering and by appropriate choice of a regularization parameter at each iteration. In this paper we describe a weighted generalized cross validation (WGCV) method for choosing the parameter. Using this method we demonstrate that the semi-convergence behavior of the Lanczos method can be overcome, making the solution less sensitive to the number of iterations.

/pdf/a-weighted-gcv-method-for-lanczos-hybrid-regularization-56z5tklocu.pdf

A weighted-GCV method for Lanczos-hybrid regularization.

The process of combining, via mathematical software tools, a set of low-resolution images into a single high-resolution image is often referred to as super-resolution. Algorithms for super-resolution involve two key steps: registration and reconstruction. Most approaches proposed in the literature decouple these steps, solving each independently. This can be effective if there are very simple, linear displacements between the low-resolution images. However, for more complex, nonlinear, nonuniform transformations, estimating the displacements can be very difficult, leading to severe inaccuracies in the reconstructed high-resolution image. This paper presents a mathematical framework and optimization algorithms that can be used to jointly estimate these quantities. Efficient implementation details are considered, and numerical experiments are provided to illustrate the effectiveness of our approach.

/pdf/numerical-methods-for-coupled-super-resolution-53fvvhu4fg.pdf

Numerical methods for coupled super-resolution

We present an efficient iterative approach to solving separable nonlinear least squares problems that arise in large-scale inverse problems. A variable projection Gauss-Newton method is used to solve the nonlinear least squares problem, and Tikhonov regularization is incorporated using an iterative hybrid scheme. Regularization parameters are chosen automatically using a weighted generalized cross validation method, thus providing a nonlinear solver that requires very little input from the user. Applications from image deblurring and digital tomosynthesis illustrate the effectiveness of the resulting numerical scheme.

An Efficient Iterative Approach for Large-Scale Separable Nonlinear Inverse Problems

We develop a hybrid iterative approach for computing solutions to large-scale ill-posed inverse problems via Tikhonov regularization. We consider a hybrid LSMR algorithm, where Tikhonov regularization is applied to the LSMR subproblem rather than the original problem. We show that, contrary to standard hybrid methods, hybrid LSMR iterates are not equivalent to LSMR iterates on the directly regularized Tikhonov problem. Instead, hybrid LSMR leads to a different Krylov subspace problem. We show that hybrid LSMR shares many of the benefits of standard hybrid methods such as avoiding semiconvergence behavior. In addition, since the regularization parameter can be estimated during the iterative process, it does not need to be estimated a priori, making this approach attractive for large-scale problems. We consider various methods for selecting regularization parameters and discuss stopping criteria for hybrid LSMR, and we present results from image processing.

A Hybrid LSMR Algorithm for Large-Scale Tikhonov Regularization

We develop a generalized hybrid iterative approach for computing solutions to large-scale Bayesian inverse problems. We consider a hybrid algorithm based on the generalized Golub--Kahan bidiagonalization for computing Tikhonov regularized solutions to problems where explicit computation of the square root and inverse of the covariance kernel for the prior covariance matrix is not feasible. This is useful for large-scale problems where covariance kernels are defined on irregular grids or are available only via matrix-vector multiplication, e.g., those from the Matern class. We show that iterates are equivalent to LSQR iterates applied to a directly regularized Tikhonov problem, after a transformation of variables, and we provide connections to a generalized singular value decomposition filtered solution. Our approach shares many benefits of standard hybrid methods such as avoiding semiconvergence and automatically estimating the regularization parameter. Numerical examples from image processing demonstrate...

Julianne Chung

Papers

A weighted-GCV method for Lanczos-hybrid regularization.

Numerical methods for coupled super-resolution

An Efficient Iterative Approach for Large-Scale Separable Nonlinear Inverse Problems

A Hybrid LSMR Algorithm for Large-Scale Tikhonov Regularization

Generalized Hybrid Iterative Methods for Large-Scale Bayesian Inverse Problems