Deblurring images. Matrices, spectra, and filtering.

*(English)*Zbl 1112.68127
Fundamentals of Algorithms 3. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM) (ISBN 978-0-898716-18-4/pbk; 978-0-89871-887-4/ebook). xiv, 130 p. (2006).

Publisher’s description: When we use a camera, we want the recorded image to be a faithful representation of the scene that we see, but every image is more or less blurry. In image deblurring, the goal is to recover the original, sharp image by using a mathematical model of the blurring process. The key issue is that some information on the lost details is indeed present in the blurred image, but this “hidden” information can be recovered only if we know the details 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. The concise MATLAB implementations described in the book provide a template of techniques that can be used to restore blurred images from many applications.

This book’s treatment of image deblurring is unique in two ways: it includes algorithmic and implementation details; and by keeping the formulations in terms of matrices, vectors, and matrix computations, it makes the material accessible to a wide range of readers. 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.

With a focus on practical and efficient algorithms, Deblurring Images: Matrices, Spectra, and Filtering includes many examples, sample image data, and MATLAB codes that allow readers to experiment with the algorithms. It also incorporates introductory material, such as how to manipulate images within the MATLAB environment, making it a stand-alone text. Pointers to the literature are given for techniques not covered in the book.

This book’s treatment of image deblurring is unique in two ways: it includes algorithmic and implementation details; and by keeping the formulations in terms of matrices, vectors, and matrix computations, it makes the material accessible to a wide range of readers. 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.

With a focus on practical and efficient algorithms, Deblurring Images: Matrices, Spectra, and Filtering includes many examples, sample image data, and MATLAB codes that allow readers to experiment with the algorithms. It also incorporates introductory material, such as how to manipulate images within the MATLAB environment, making it a stand-alone text. Pointers to the literature are given for techniques not covered in the book.