Method For Image Deblurring Research Articles

Image restoration

AbstractTrue images are usually degraded during image acquisition. Image restoration is for restoring true images from their observed but degraded versions; it is often used for preprocessing observed images so that subsequent image processing and analysis become more reliable. Among many different types of degradations, point degradations (or noise) and spatial degradations (or blurring) are most common in applications. This article introduces some fundamental image denoising and image deblurring methods. Copyright © 2009 John Wiley & Sons, Inc.This article is categorized under: Data: Types and Structure > Image and Spatial Data

Linearized Bregman Iterations for Frame-Based Image Deblurring

Real images usually have sparse approximations under some tight frame systems derived from framelets, an oversampled discrete (window) cosine, or a Fourier transform. In this paper, we propose a method for image deblurring in tight frame domains. It is reduced to finding a sparse solution of a system of linear equations whose coefficient matrix is rectangular. Then, a modified version of the linearized Bregman iteration proposed and analyzed in [J.-F. Cai, S. Osher, and Z. Shen, Math. Comp., to appear, UCLA CAM Report (08-52), 2008; J.-F. Cai, S. Osher, and Z. Shen, Math. Comp., to appear, UCLA CAM Report (08-06), 2008; S. Osher et al., UCLA CAM Report (08-37), 2008; W. Yin et al., SIAM J. Imaging Sci., 1 (2008), pp. 143–168] can be applied. Numerical examples show that the method is very simple to implement, robust to noise, and effective for image deblurring.

Deconvolution methods for image deblurring in optical coherence tomography

Two-dimensional deconvolution methods are proposed to deblur optical coherence tomography images. One employs a two-dimensional deconvolution with a matrix given by the product of the longitudinal and transversal point-spread functions as its kernel, which can be taken as the general point-spread function of an optical coherence tomography system. The other uses two one-dimensional deconvolutions with the longitudinal and transversal point-spread functions successively. It is shown that the two deconvolution methods can deblur the experimentally obtained optical coherence tomography images effectively.

Cascadic Multiresolution Methods for Image Deblurring

This paper investigates the use of cascadic multiresolution methods for image deblurring. Iterations with a conjugate gradient-type method are carried out on each level, and terminated by a stopping rule based on the discrepancy principle. Prolongation is carried out by nonlinear edge-preserving operators, which are defined via PDEs associated with Perona–Malik or total variation-type models. Computed examples demonstrate the effectiveness of the methods proposed.

Least-squares methods with Poissonian noise: Analysis and comparison with the Richardson-Lucy algorithm

It is well-known that the noise associated with the collection of an astronomical image by a CCD camera is largely Poissonian. One would expect, therefore, that computational approaches that incorporate this a priori information will be more effective than those that do not. The Richardson-Lucy (RL) algorithm, for example, can be viewed as a maximum-likelihood (ML) method for image deblurring when the data noise is assumed to be Poissonian. Least-squares (LS) approaches, on the other hand, are based on the assumption that the noise is Gaussian with fixed variance across pixels, which is rarely accurate. Given this, it is surprising that in many cases results obtained using LS techniques are relatively insensitive to whether the noise is Poissonian or Gaussian. Furthermore, in the presence of Poisson noise, results obtained using LS techniques are often comparable with those obtained by the RL algorithm. We seek an explanation of these phenomena via an examination of the regularization properties of particular LS algorithms. In addition, a careful analysis of the RL algorithm yields an explanation as to why it is more effective than LS approaches for star-like objects, and why it provides similar reconstructions for extended objects. Finally a comparative convergence analysis of the two algorithms is carried out, with a section devoted to the convergence properties of the RL algorithm. Numerical results are presented throughout the paper. The subject treated in this paper is not purely academic. In comparison with many ML algorithms, the LS algorithms are much easier to use and to implement, are computationally more efficient, and are more flexible regarding the incorporation of constraints on the solution. Consequently, if little to no improvement is gained in the use of an ML approach over an LS algorithm, the latter will often be the preferred approach.

Iterative Methods for Image Deblurring: A Matlab Object-Oriented Approach

In iterative image restoration methods, implementation of efficient matrix vector multiplication, and linear system solves for preconditioners, can be a tedious and time consuming process. Different blurring functions and boundary conditions often require implementing different data structures and algorithms. A complex set of computational methods is needed, each likely having different input parameters and calling sequences. This paper describes a set of Matlab tools that hide these complicated implementation details. Combining the powerful scientific computing and graphics capabilities in Matlab, with the ability to do object-oriented programming and operator overloading, results in a set of classes that is easy to use, and easily extensible.

Iterative methods for image deblurring

The authors discuss the use of iterative restoration algorithms for the removal of linear blurs from photographic images that may also be assumed to be degraded by pointwise nonlinearities such as film saturation and additive noise. Iterative algorithms allow for the incorporation of various types of prior knowledge about the class of feasible solutions, can be used to remove nonstationary blurs, and are fairly robust with respect to errors in the approximation of the blurring operator. Special attention is given to the problem of convergence of the algorithms, and classical solutions such as inverse filters, Wiener filters, and constrained least-squares filters are shown to be limiting solutions of variations of the iterations. Regularization is introduced as a means for preventing the excessive noise magnification that is typically associated with ill-conditioned inverse problems such as the deblurring problem, and it is shown that noise effects can be minimized by terminating the algorithms after a finite number of iterations. The role and choice of constraints on the class of feasible solutions are also discussed.