Advances in sampling theory and techniques / Leonid P. Yaroslavsky.

Format:

Book

Author/Creator:

I͡Aroslavskiĭ, L. P. (Leonid Pinkhusovich), author.

Contributor:

Society of Photo-optical Instrumentation Engineers, publisher.

Series:

SPIE Press monograph ; PM315.

SPIE Press monograph ; PM315

Language:

English

Subjects (All):

Image processing--Digital techniques--Mathematics.

Image processing.

Signal processing--Digital techniques--Mathematics.

Signal processing.

Fourier transformations.

Physical Description:

1 online resource (212 pages) : illustrations

Place of Publication:

Bellingham, Washington : SPIE, [2020]

Summary:

"This book presents the current state of the art of digital engineering, as well as recent proposals for optimal methods of signal and image non-redundant sampling and interpolation-error-free resampling. Topics include classical sampling theory, conventional sampling, the peculiarities of sampling 2D signals, artifacts, compressed sensing, fast algorithms, the discrete uncertainty principle, and sharply-band-limited discrete signals and basis functions with sharply limited support. Exercises based in MATLAB supplement the text throughout"-- Provided by publisher.

Contents:

Preface

1. Introduction: 1.1. A historical perspective of sampling: from ancient mosaics to computational imaging; 1.2. Book overview

Part I: Signal sampling: 2. Sampling theorems: 2.1. Kotelnikov / Shannon sampling theorem: sampling band-limited 1D signals; 2.2. Sampling 1D band-pass signals; 2.3. Sampling band-limited 2D signals; optimal regular sampling lattices; 2.4. Sampling real signals; signal reconstruction distortions due to spectral aliasing; 2.5. The sampling theorem in a realistic reformulation; 2.6. Image sampling with a minimal sampling rate by means of image sub-band decomposition; 2.7. The discrete sampling theorem and its generalization to continuous signals; 2.8. Exercises

3. Compressed sensing demystified: 3.1. Redundancy of regular image sampling and image spectra sparsity; 3.2. Compressed sensing: why and how it is possible to precisely reconstruct signals sampled with aliasing; 3.3. Compressed sensing and the problem of minimizing the signal sampling rate; 3.4. Exercise

4. Image sampling and reconstruction with sampling rates close to the theoretical minimum: 4.1. The ASBSR method of image sampling and reconstruction; 4.2. Experimental verification of the method; 4.3. Some practical issues; 4.4. Other possible applications of the ASBSR method of image sampling and reconstruction; 4.5. Exercises

5. Signal and image resampling, and building their continuous models: 5.1. Signal/image resampling as an interpolation problem; convolutional interpolators; 5.2. Discrete sinc interpolation: a gold standard for signal resampling; 5.3. Fast algorithms of discrete sinc interpolation and their applications; 5.4. Discrete sinc interpolation versus other interpolation methods: performance comparison; 5.5. Exercises

6. Discrete sinc interpolation in other applications and implementations: 6.1. Precise numerical differentiation and integration of sampled signals; 6.2. Local ("elastic") image resampling: sliding-window discrete sinc interpolation algorithms; 6.3. Image data resampling for image reconstruction from projections; 6.4. Exercises

7. The discrete uncertainty principle, sinc-lets, and other peculiar properties of sampled signals: 7.1. The discrete uncertainty principle; 7.2. Sinc-lets: Sharply-band-limited basis functions with Sharply limited support; 7.3. Exercises

Part II: Discrete representation of signal transformations: 8. Basic principles of discrete representation of signal transformations

9. Discrete representation of the convolution integral: 9.1. Discrete convolution; 9.2. Point spread functions and frequency responses of digital filters; 9.3. Treatment of signal borders in digital convolution

10. Discrete representation of the Fourier integral transform: 10.1. 1D discrete Fourier transforms; 10.2. 2D discrete Fourier transforms; 10.3. Discrete cosine transform; 10.4. Boundary-effect-free signal convolution in the DCT domain; 10.5. DFT and discrete frequency responses of digital filters; 10.6. Exercises

Appendix 1. Fourier series, integral fourier transform, and delta function: A1.1. 1D Fourier series; A1.2. 2D Fourier series; A1.3. 1D integral Fourier transform; A1.4. 2D integral Fourier transform; A1.5. Delta function, sinc function, and the ideal low-pass filter; A1.6. Poisson summation formula

Appendix 2. Discrete Fourier transforms and their properties: A2.1. Invertibility of discrete Fourier transforms and the discrete sinc function; A2.2. The Parseval's relation for the DFT; A2.3. Cyclicity of the DFT; A2.4. Shift theorem; A2.5. Convolution theorem; A2.6. Symmetry properties; A2.7. SDFT spectra of sinusoidal signals; A2.8. Mutual correspondence between the indices of ShDFT spectral coefficients and signal frequencies; A2.9. DFT spectra of sparse signals and spectral zero-padding; A2.10. Invertibility of the shifted DFT and signal resampling; A2.11. DFT as a spectrum analyzer; A2.12. Quasi-continuous spectral analysis; A2.13. Signal resizing and rotation capability of the rotated scaled DFT; A2.14. Rotated and scaled DFT as digital convolution

References

Index.

Notes:

Includes bibliographical references and index.

Title from PDF title page (SPIE eBooks Website, viewed 2020-01-28).

ISBN:

1-5231-3387-2

1-5106-3384-7

OCLC:

1139240737