In image deblurring, the goal is to recover the original, sharp image by using a mathematical model of the blurring process. Deblurring Images: Matrices, Spectra, and Filtering describes the deblurring algorithms and techniques collectively known as spectral filtering methods, in which the singular value decomposition—or a similar decomposition with spectral properties—is used to introduce the necessary regularization or filtering in the reconstructed image. Students and researchers in engineering will gain an understanding of the linear algebra behind filtering methods, while readers in applied mathematics, numerical analysis, and computational science will be exposed to modern techniques to solve realistic large-scale problems in image processing. Pointers to the literature are given for techniques not covered in the book. The book describes the algorithms and techniques collectively known as spectral filtering methods, in which the singular value decomposition—or a similar decomposition with spectral properties—is used to introduce the necessary regularization or filtering in the reconstructed image.

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Auxiliary Functions Bibliography Index PrefaceThere is nothing worse than a sharp image of a fuzzy concept. The book describes the algorithms and techniques collectively known as spectral filtering methods, in which the singular value decompositionor a similar decomposition with spectral propertiesis used to introduce the necessary regularization or filtering in the reconstructed image.

The main purpose of the book is to give students and engineers an understanding of the linear algebra behind the filtering methods. Readers in applied mathematics, numerical analysis, and computational science will be exposed to modern techniques to solve realistic large-scale problems in image deblurring.

The book is intended for beginners in the field of image restoration and regularization. While the underlying mathematical model is an ill-posed problem in the form of an integral equation of the first kind for which there is a rich theory , we have chosen to keep our formulations in terms of matrices, vectors, and matrix computations.

Our reasons for this choice of formulation are twofold: 1 the linear algebra terminology is more accessible to many of our readers, and 2 it is much closer to the computational tools that are used to solve the given problems. Throughout the book we give references to the literature for more details about the problems, the techniques, and the algorithmsincluding the insight that is obtained from studying the underlying ill-posed problems.

All the methods presented in this book belong to the general class of regularization methods, which are methods specially designed for solving ill-posed problems.

We do not require the reader to be familiar with these regularization methods or with ill-posed problems. For readers who already have this knowledge, we aim to give a new and practical perspective on the issues of using regularization methods to solve real problems. The topics covered in our book are well suited for computer demonstrations, and our aim is that the reader will be able ix.

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## DEBLURRING IMAGES MATRICES SPECTRA AND FILTERING PDF

In image deblurring, the goal is to recover the original, sharp image by using a mathematical model of the blurring process. Deblurring Images: Matrices, Spectra, and Filtering describes the deblurring algorithms and techniques collectively known as spectral filtering methods, in which the singular value decomposition—or a similar decomposition with spectral properties—is used to introduce the necessary regularization or filtering in the reconstructed image. Students and researchers in engineering will gain an understanding of the linear algebra behind filtering methods, while readers in applied mathematics, numerical analysis, and computational science will be exposed to modern techniques to solve realistic large-scale problems in image processing. Pointers to the literature are given for techniques not covered in the book. The book describes the algorithms and techniques collectively known as spectral filtering methods, in which the singular value decomposition—or a similar decomposition with spectral properties—is used to introduce the necessary regularization or filtering in the reconstructed image. The main purpose of the book is to give students and engineers an understanding of the linear algebra behind the filtering methods.

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## deblurring images, matrices, spectra, and filtering (fundamentals of algorithms)

Tushicage He has published many research papers on scientific computing, numerical linear algebra, inverse problems, and image processing. In image deblurring, the goal is to recover the original, sharp image by using a mathematical model of the blurring process. Home Fundamentals of Algorithms Deblurring Images: She is the author of over 75 publications on numerical analysis and computational science and over 25 publications on education and mentoring. A background in signal processing and a familiarity with regularization methods or with ill-posed problems are not needed. Readers will become familiar with modern techniques used to solve realistic large-scale problems in image deblurring. Based on your location, we recommend that you select: The Image Deblurring Problem 2.

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## Deblurring Images: Matrices, Spectra, and Filtering

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