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Digital Signal Processing Handbook P25

Signal recovery has been an active area of research for applications in many different scientific disciplines. A central reason for exploring the feasibility of signal recovery is due to the limitations imposed by a physical device on the amount of data one can record. For example, for | Podilchuk C. Signal Recovery from Partial Information Digital Signal Processing Handbook Ed. Vijay K. Madisetti and Douglas B. Williams Boca Raton CRC Press LLC 1999 1999 by CRC Press LLC 25 Signal Recovery from Partial Information Christine Podilchuk Bell Laboratories Lucent Technologies 25.1 Introduction 25.2 Formulation of the Signal Recovery Problem Prolate Spheroidal Wavefunctions 25.3 Least Squares Solutions WienerFiltering The Pseudoinverse Solution Regularization Techniques 25.4 Signal Recovery using Projection onto Convex Sets POCS The POCS Framework 25.5 Row-Based Methods 25.6 Block-Based Methods 25.7 Image Restoration Using POCS References 25.1 Introduction Signal recovery has been an active area of research for applications in many different scientific disciplines. A central reason for exploring the feasibility of signal recovery is due to the limitations imposed by a physical device on the amount of data one can record. For example for diffractionlimited systems the finite aperture size of the lens constrains the amount of frequency information that can be captured. The image degradation is due to attenuation of high frequency components resulting in a loss of details and other high frequency information. In other words the finite aperture size of the lens acts like a lowpass filter on the input data. In some cases the quality of the recorded image data can be improved by building a more costly recording device but many times the required condition for acceptable data quality is physically unrealizable or too costly. Other times signal recovery may be necessary is for the recording of a unique event that cannot be reproduced under more ideal recording conditions. Some of the earliest work on signal recovery includes the work by Sondhi 1 and Slepian 2 on recovering images from motion blur and Helstrom 3 on least squares restoration. A sampling of some of the signal recovery algorithms applied to different types of problems can be found in 4 21 . Further