Book Reviews

Deblurring Images: Matrices, Spectra and Filtering

J. Electron. Imaging. 17(1), 019901 (April 02, 2008). doi:10.1117/1.2900557
History: April 07, 2004; Published April 02, 2008
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This book provides an introduction into the theory and application of spectral filtering methods for image deblurring. Image deblurring belongs to a class of operations known as image restoration, which has a subtly different goal than image enhancement. Image restoration is aimed at restoring the original signal while image enhancement is typically concerned with improving or extracting image features. In the case of image deblurring the challenge is to find a balance between two competing degradations, blur and noise.

As the authors note in the preface, this text “is intended for beginners in the field of image restoration and regularization.” The authors do a good job of embracing this goal on several fronts. The first three chapters get the reader up to speed on representing an image and imaging operations with matrix equations. They address both a simple linear blur operation and several noise sources. The models and techniques in the book are developed based on the assumption that the blur is known and the noise is additive.

These early chapters also introduce the reader to some of the basics of MATLAB, especially as it relates to the processing, displaying, and writing of images. In fact, most of the theoretical material in the book is fleshed out with MATLAB examples. Sprinkled throughout the text are snippets of MATLAB code and references to MATLAB syntax and terminology. A large appendix includes commented MATLAB listings, which are also available for download on the web.

This approach, i.e., providing a theoretical introduction combined with working MATLAB examples, makes the material more accessible and enables readers to build confidence with the concepts from the beginning. Periodically throughout the text sample problems and opportunities for hands-on work are presented as challenges. Anyone who is familiar with and has access to MATLAB will quickly be able to try out the techniques and conduct their own experiments.

Chapters 4 through 6 address the heart of the material. The blur problem is first developed in detail as a structured matrix equation based on the given boundary conditions. All three boundary conditions (zero, periodic, and reflexive) are treated individually. This is followed by an introduction to spectral filtering, which naturally motivates a discussion of singular value decomposition (SVD), discrete Fourier transform (DFT), and discrete cosine transform (DCT) bases for the different boundary conditions. Not only are the theory and basic equations presented, but significant attention is also given to efficient implementation. Brute force spectral filtering of an image can be quite computationally expensive and the authors do a good job of identifying fast alternatives.

Several regularization methods are presented along with criteria for determining the regularization parameters in Chapter 6. The regularization methods are the construct for imposing regularity on the solutions to the ill-posed problem represented by deblurring. The regularization parameters are driven by an understanding of the noise in the image. Herein lays the only complaint with this book, viz., given the importance of understanding the noise, the section on estimating noise levels is too brief. Admittedly, the book, totaling 130 pages including the appendix, is brief and focused, but more detail in this section would have been appreciated. Chapter 7, the final chapter, addresses a grab bag of miscellaneous topics and extensions, including color, more generalized regularization, and the case where the blur is unknown, i.e., blind deconvolution.

Readers should be familiar with linear algebra and transforms such as SVD, and, of course, have access to MATLAB. Overall, this book is an excellent resource for someone wanting a hands-on introduction to image deblurring and spectral filtering.

Rodney Miller is a department head in the Computational Science and Technology Research Group at Kodak’s Research Labs. He holds 27 US patents in image processing. His current interests include multidimensional signal processing and computational photography.

RodneyMillerIndividualAuthor

Citation

Per Christian Hansen ; James G. Nagy and Dianne P. Leary
"Deblurring Images: Matrices, Spectra and Filtering", J. Electron. Imaging. 17(1), 019901 (April 02, 2008). ; http://dx.doi.org/10.1117/1.2900557


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