Determination of singular value truncation threshold for regularization in ill-posed problems

2020 ◽  
pp. 1-31
Author(s):  
Shuyong Duan ◽  
Botao Yang ◽  
Fang Wang ◽  
Guirong Liu
Keyword(s):  
Singular Value ◽  
Ill Posed ◽  
Truncation Threshold

Information and estimation in image processing

1987 ◽  
Vol 45 ◽  
pp. 14-17
Author(s):  
B. Roy Frieden
Keyword(s):  
Image Processing ◽  
Optical System ◽  
Large Amplitude ◽  
Communication Theory ◽  
Image Data ◽  
Direct Approach ◽  
Ill Posed

Despite the skill and determination of electro-optical system designers, the images acquired using their best designs often suffer from blur and noise. The aim of an “image enhancer” such as myself is to improve these poor images, usually by digital means, such that they better resemble the true, “optical object,” input to the system. This problem is notoriously “ill-posed,” i.e. any direct approach at inversion of the image data suffers strongly from the presence of even a small amount of noise in the data. In fact, the fluctuations engendered in neighboring output values tend to be strongly negative-correlated, so that the output spatially oscillates up and down, with large amplitude, about the true object. What can be done about this situation? As we shall see, various concepts taken from statistical communication theory have proven to be of real use in attacking this problem. We offer below a brief summary of these concepts.

scholarly journals A modified truncation singular value decomposition method for solving ill-posed problems

2018 ◽  
Vol 13 ◽  
pp. 174830181881360 ◽  
Author(s):  
Zhenyu Zhao ◽  
Riguang Lin ◽  
Zehong Meng ◽  
Guoqiang He ◽  
Lei You ◽  
...  
Keyword(s):  
Singular Value Decomposition ◽  
Decomposition Method ◽  
Singular Value ◽  
Numerical Results ◽  
New Method ◽  
Truncated Singular Value Decomposition ◽  
Singular Value Decomposition Method ◽  
Ill Posed ◽  
Value Decomposition

A modified truncated singular value decomposition method for solving ill-posed problems is presented in this paper, in which the solution has a slightly different form. Both theoretical and numerical results show that the limitations of the classical TSVD method have been overcome by the new method and very few additive computations are needed.

scholarly journals Determination of source term for fractional heat equation on the sphere

2020 ◽  
Vol 24 (Suppl. 1) ◽  
pp. 361-370
Author(s):  
Nguyen Phuong ◽  
Tran Binh ◽  
Nguyen Luc ◽  
Nguyen Can
Keyword(s):  
Diffusion Equation ◽  
Heat Equation ◽  
Exact Solutions ◽  
Source Term ◽  
Fractional Diffusion ◽  
Inverse Source Problem ◽  
Fractional Heat Equation ◽  
Ill Posed ◽  
Time Fractional Diffusion Equation

In this work, we study a truncation method to solve a time fractional diffusion equation on the sphere of an inverse source problem which is ill-posed in the sense of Hadamard. Through some priori assumption, we present the error estimates between the regularized and exact solutions.

Determination of componentwise chromatographic elution regions using singular value evolving profiles

1996 ◽  
Vol 334 (1-2) ◽  
pp. 15-25 ◽  
Author(s):  
Gregory A. Bakken ◽  
Nickey J. Messick ◽  
John H. Kalivas
Keyword(s):  
Singular Value ◽  
Chromatographic Elution

scholarly journals Determination of conductivity in a heat equation

2000 ◽  
Vol 24 (9) ◽  
pp. 589-594 ◽  
Author(s):  
Ping Wang ◽  
Kewang Zheng
Keyword(s):  
Numerical Simulation ◽  
Inverse Problem ◽  
Approximate Solution ◽  
Heat Equation ◽  
Ill Posed ◽  
Smooth Data

We consider the problem of determining the conductivity in a heat equation from overspecified non-smooth data. It is an ill-posed inverse problem. We apply a regularization approach to define and construct a stable approximate solution. We also conduct numerical simulation to demonstrate the accuracy of our approximation.

scholarly journals On the application of singular value decomposition and Tikhonov regularization to ill-posed problems in hyperbolic passive location

2013 ◽  
Vol 57 (7-8) ◽  
pp. 1999-2008 ◽  
Author(s):  
Ivan A. Mantilla-Gaviria ◽  
Mauro Leonardi ◽  
Juan V. Balbastre-Tejedor ◽  
Elías de los Reyes
Keyword(s):  
Singular Value Decomposition ◽  
Tikhonov Regularization ◽  
Singular Value ◽  
Passive Location ◽  
Ill Posed ◽  
Value Decomposition
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