Digital Image Reconstruction in the Spectral Domain Utilizing the Moore‐Penrose Inverse

Chountasis, Spiros; Katsikis, Vasilios N.; Pappas, Dimitrios

doi:10.1155/2010/750352

Cited by 32 publications

(31 citation statements)

References 14 publications

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“…Applications of this last method to astronomical data analysis can be found in [21,20,22,23] and applications to gene expression analysis can be found in [25,26]. Image compression algorithms using SVD are known at least since [27] and digital image restoration using the Moore-Penrose pseudoinverse have been studied in [28,29].…”

Section: Some Applications Of the Moore-penrose Pseudoinversementioning

confidence: 99%

The Moore–Penrose Pseudoinverse: A Tutorial Review of the Theory

2011

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In the last decades the Moore-Penrose pseudoinverse has found a wide range of applications in many areas of Science and became a useful tool for physicists dealing, for instance, with optimization problems, with data analysis, with the solution of linear integral equations, etc. The existence of such applications alone should attract the interest of students and researchers in the Moore-Penrose pseudoinverse and in related subjects, like the singular values decomposition theorem for matrices. In this note we present a tutorial review of the theory of the Moore-Penrose pseudoinverse. We present the first definitions and some motivations and, after obtaining some basic results, we center our discussion on the Spectral Theorem and present an algorithmically simple expression for the computation of the Moore-Penrose pseudoinverse of a given matrix. We do not claim originality of the results. We rather intend to present a complete and self-contained tutorial review, useful for those more devoted to applications, for those more theoretically oriented and for those who already have some working knowledge of the subject.

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Section: Some Applications Of the Moore-penrose Pseudoinversementioning

confidence: 99%

The Moore–Penrose Pseudoinverse: A Tutorial Review of the Theory

2011

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“…the Moore-Penrose solution) of the matrix equation (2.2), and it is investigated in [4,5]. Furthermore, we have observed in [19,20] that the operator E(Y) frequently gives a better improvement of blurred image with respect to restoration contained in Y.…”

Section: Mathematical Modelsmentioning

confidence: 99%

“…This approach was firstly used in [4,5]. A simplified implementation of the partitioning method on this class of Toeplitz matrices is described in [21].…”

Section: Introductionmentioning

confidence: 99%

On removing blur in images using least squares solutions

Stanimirović

Stojanović

Pappas

et al. 2016

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Abstract.The further investigation of the image restoration method introduced in [19,20] is presented in this paper. Continuing investigations in that area, two additional applications of the method are investigated. More precisely, we consider the possibility to replace the available matrix in the method by the restoration obtained applying the Tikhonov regularization method or the Truncated Singular Value decomposition method. Additionally, statistical analysis of numerical results generated by applying the proposed improvement of image restoration methods is presented. Previously performed numerical experiments as well as new numerical results and the statistical analysis confirm that the least squares approach can be used as a useful tool for improving restored images obtained by other image restoration methods.

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“…The methods of image restoration, based on the usage of the Moore-Penrose inverse, have been exploited in many recent papers [6][7][8]. Several methods for computing the Moore-Penrose inverse have been introduced in [2].…”

Section: Introductionmentioning

confidence: 99%

“…The unique vectorf satisfying (3) represents a row of the restored image [5][6][7][8], and it is defined bỹ…”

Section: Introductionmentioning

confidence: 99%

Application of the pseudoinverse computation in reconstruction of blurred images

Miljković¹,

Miladinović²,

Stanimirović³

et al. 2012

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Abstract. We present a direct method for removing uniform linear motion blur from images. The method is based on a straightforward construction of the Moore-Penrose inverse of the blurring matrix for a given mathematical model. The computational load of the method is decreased significantly with respect to other competitive methods, while the resolution of the restored images remains at a very high level. The method is implemented in the programming package MATLAB and respective numerical examples are presented.

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Digital Image Reconstruction in the Spectral Domain Utilizing the Moore‐Penrose Inverse

Cited by 32 publications

References 14 publications

The Moore–Penrose Pseudoinverse: A Tutorial Review of the Theory

The Moore–Penrose Pseudoinverse: A Tutorial Review of the Theory

On removing blur in images using least squares solutions

Application of the pseudoinverse computation in reconstruction of blurred images

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