Prakash Ishwar

Dr. Prakash Ishwar

Beckman Institute for Advanced Science and Technology

University of Illinois


Wednesday, March 13
3:00 - 4:00 P.M.
Room 1005 EECS

Statistical signal modeling and estimation using multiple wavelet bases and the maximum entropy principle


Compression, quality enhancement, hashing, searching, classification, and copyright protection algorithms are some of the principal ingredients of many multimedia applications. These algorithms make use of signal models (explicit or implied) based on some prior knowledge about signal characteristics. The performance of these algorithms directly depends upon the capacity of the underlying model to capture a wide variety of signal features such as location of edges or discontinuities, limited spatial/chromatic intensity range, frequency support, compact representations in specific families of orthonormal bases, camera motion, etc. The sheer variety and complexity of multimedia signal content makes the task of developing effective signal models rather challenging.

My Ph. D. thesis explores ideas of "fusing'' information from diverse signal attributes into a representative model for specific signal classes of interest e.g. "natural'' images - pictures of complex natural scenes that are typically statistically nonstationary. To this end we propose a general estimation framework based on the maximum entropy principle. We provide new sufficient conditions that guarantee the existence of the maxent distribution and also provide an analytical characterization. We demonstrate a fundamental equivalence between two seemingly different approaches for estimation, namely maximum a posteriori estimation using a maximum entropy prior and set-theoretic estimation. We develop a rich class of priors for natural images from bounds on the expected values of certain general energy functions in several orthonormal wavelet bases. We present experimental results for the problem of image restoration in additive white Gaussian noise. Our results indicate significant improvements both in terms of mean square error as well as perceptual quality. We are able to show under some conditions how some traditional image denoising algorithms are subsumed by our information fusion framework.


Prakash Ishwar received the B. Tech. degree in electrical engineering from the Indian Institute of Technology, Bombay, India, in 1996, and the M.S. degree in electrical and computer engineering from University of Illinois at Urbana-Champaign, in 1998. Since 1996, he has been a research assistant in the department of electrical and computer engineering and the Beckman Institute at the University of Illinois. He was with IBM's Watson Research Center as an intern in 2000. His fields of professional interest are image and video processing, compression, statistical signal modeling and processing, information theory, and the application of multiresolution signal analysis and optimization theory to these areas. He was awarded the Frederic T. and Edith F. Mavis College of Engineering Fellowship of the University of Illinois in 2000.

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