From the Publisher: 
For this inexpensive paperback edition of a groundbreaking classic, the author has extensively rearranged, rewritten and enlarged the material. Book is unique in its emphasis on the frequency approach and its use in the solution of problems. Contents include: Fundamentals and Algorithms; Polynomial Approximation Classical Theory; Fourier ApproximationModern Therory; Exponential Approximation.

Numerical Methods for Scientists and Engineers

In recent years, tree-structured analysis/reconstruction systems have been extensively studied for use in subband coders for speech. In such systems, it is important that the individual channel signals be decimated in such a way that the number of samples coded and transmitted does not exceed the number of samples in the original speech signal. Under this constraint, the systems presented in the past have sought to remove the aliasing distortion while minimizing the overall analysis/reconstruction distortion. In this paper, it is shown that it is possible to design tree-structured analysis/reconstruction systems which meet the sampling rate condition and which also result in exact reconstruction of the input signal. This paper develops the conditions for exact reconstruction and presents a general method for designing the corresponding high quality analysis and reconstruction filters.

A procedure for designing exact reconstruction filter banks for tree-structured subband coders

In this paper, we propose an empirical identification method of the Gaussian blur parameter for image deblurring. The parameter estimate is chosen from a collection of candidate parameters. The blurred image is restored by these candidate parameters under the assumption that the candidate is equal to the true value. The estimate is selected to be at the maximum point of the differential coefficients of restored image Laplacian L1 norm curve. Experimental results are presented to demonstrate the performance of the proposed method.

An Empirical Identification Method of Gaussian Blur Parameter for Image Deblurring

Imagery acquired with modern imaging systems is susceptible to a variety of degradations, including blur from the point
spread function (PSF) of the imaging system, aliasing from undersampling, blur and warping from atmospheric
turbulence, and noise. A variety of image restoration methods have been proposed that estimate an improved image by
processing a sequence of these degraded images. In particular, multi-frame image restoration has proven to be a
particularly powerful tool for atmospheric turbulence mitigation (TM) and super-resolution (SR). However, these
degradations are rarely addressed simultaneously using a common algorithm architecture, and few TM or SR solutions
are capable of performing robustly in the presence of true scene motion, such as moving dismounts. Still fewer TM or
SR algorithms have found their way into practical real-time implementations. In this paper, we describe a new L-3 joint
TM and SR (TMSR) real-time processing solution and demonstrate its capabilities. The system employs a recently
developed versatile multi-frame joint TMSR algorithm that has been implemented using a real-time, low-power FPGA
processor system. The L-3 TMSR solution can accommodate a wide spectrum of atmospheric conditions and can
robustly handle moving vehicles and dismounts. This novel approach unites previous work in TM and SR and also
incorporates robust moving object detection. To demonstrate the capabilities of the TMSR solution, results using field
test data captured under a variety of turbulence levels, optical configurations, and applications are presented. The
performance of the hardware implementation is presented, and we identify specific insertion paths into tactical sensor
systems.

A real-time atmospheric turbulence mitigation and super-resolution solution for infrared imaging systems

A critical assumption in applying Godard CMA algorithm for blind deconvolution and equalization is the assumption of an independently distributed source. Almost all the applications in the literature have based their implementations on this assumption. To our knowledge, no research has been done on the effect of source correlation on adaptive blind deblurring of images through CMA, and this paper addresses that gap, coming up with a novel model of addressing the source correlation problem in the image deblurring through CMA.

Minimum Kurtosis CMA Deconvolution for Blind Image Restoration

To my mom, Mei, my wife, Nan and in memory of my grandma, Yanqing for all of your love iii ACKNOWLEDGEMENTS I would like to thank Prof. Stanley Reeves of Auburn university who provided help with the implementation of Generalized Cross Validation (GCV). There are many helpful feedbacks from the readers of our papers. For example, Lalaké Apoyan pointed out the scintillation effects of turbulence. Mathworks, Philips Research Lab for offering me the internships during my degree program. Very special thanks go to Dr. Steven Simske from HP lab for his support and encouragement throughout my program. loved, encouraged, and motivated me through all the ups and downs in my life. They had confidence in me when I had little confidence in myself. I thank my dogs, Kelly, Vanilla and Cookie for making our lives more enjoyable.

Restoration of Atmospheric Turbulence Degraded Video using Kurtosis Minimization and Motion Compensation

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Restoration of Atmospheric Turbulence Degraded Video using Kurtosis Minimization and Motion Compensation