• Corpus ID: 246240070

The Image Deblurring Problem: Matrices, Wavelets, and Multilevel Methods

@article{Austin2022TheID,
  title={The Image Deblurring Problem: Matrices, Wavelets, and Multilevel Methods},
  author={David L. Austin and Malena I. Espa{\~n}ol and Mirjeta Pasha},
  journal={ArXiv},
  year={2022},
  volume={abs/2201.09831}
}
The image deblurring problem consists of reconstructing images from blur and noise contaminated available data. In this AMS Notices article, we provide an overview of some well known numerical linear algebra techniques that are use for solving this problem. In particular, we start by carefully describing how to represent images, the process of blurring an image and modeling different kind of added noise. Then, we present regularization methods such as Tikhonov (on the standard and general form… 

References

SHOWING 1-10 OF 21 REFERENCES
A Multilevel Algorithm for Simultaneously Denoising and Deblurring Images
TLDR
A fast multilevel Denoising method is generalized to solving the minimization model for simultaneously denoising and deblurring images under the total variation regularization by a detailed study of the structured matrices that are associated with the blurring operator.
Multilevel Approach For Signal Restoration Problems With Toeplitz Matrices
TLDR
A multilevel method for discrete ill-posed problems arising from the discretization of Fredholm integral equations of the first kind using the Haar wavelet transform to define restriction and prolongation operators within a multigrid-type iteration.
Cascadic Multiresolution Methods for Image Deblurring
TLDR
This paper investigates the use of cascadic multiresolution methods for image deblurring using nonlinear edge-preserving operators defined via PDEs associated with Perona-Malik or total variation-type models.
Reconstruction of noisy and blurred images using blur kernel
TLDR
This work uses sparse representation to identify the blur kernel using radon transformation and Fourier for the length calculation of the image and uses Lucy Richardson algorithm which is also called NON-Blind(NBID) Algorithm for more clean and less noisy image output.
On the Regularizing Power of Multigrid-type Algorithms
TLDR
This work considers the deblurring problem of noisy and blurred images in the case of known space invariant point spread functions with four choices of boundary conditions and defines an iterative regularizing method which can choose multigrid procedures which are much more efficient than classical techniques without losing accuracy in the restored image.
Efficient edge-preserving methods for dynamic inverse problems
We consider efficient methods for computing solutions to dynamic inverse problems, where both the quantities of interest and the forward operator (measurement process) may change at different time
Computational Methods for Inverse Problems
In verse problems arise in a number of important practical applications, ranging from biomedical imaging to seismic prospecting. This book provides the reader with a basic understanding of both the
Discrete Inverse Problems: Insight and Algorithms
Inverse problems arise when we reconstruct a sharper image from a blurred one or reconstruct the underground mass density from measurements of the gravity above the ground. When we solve an inverse
Bilevel Optimization, Deep Learning and Fractional Laplacian Regularization with Applications in Tomography
TLDR
The key advantage of using fractional Laplacian as a regularizer is that it leads to a linear operator, as opposed to the total variation regularization which results in a nonlinear degenerate operator.
The Use of the L-Curve in the Regularization of Discrete Ill-Posed Problems
TLDR
A unifying characterization of various regularization methods is given and it is shown that the measurement of “size” is dependent on the particular regularization method chosen, and a new method is proposed for choosing the regularization parameter based on the L-curve.
...
...