Russell M. Mersereau

Iterative methods for image deblurring

The authors discuss the use of iterative restoration algorithms for the removal of linear blurs from photographic images that may also be assumed to be degraded by pointwise nonlinearities such as film saturation and additive noise. Iterative algorithms allow for the incorporation of various types of prior knowledge about the class of feasible solutions, can be used to remove nonstationary blurs, and are fairly robust with respect to errors in the approximation of the blurring operator. Special attention is given to the problem of convergence of the algorithms, and classical solutions such as inverse filters, Wiener filters, and constrained least-squares filters are shown to be limiting solutions of variations of the iterations. Regularization is introduced as a means for preventing the excessive noise magnification that is typically associated with ill-conditioned inverse problems such as the deblurring problem, and it is shown that noise effects can be minimized by terminating the algorithms after a finite number of iterations. The role and choice of constraints on the class of feasible solutions are also discussed. >

The processing of hexagonally sampled two-dimensional signals

Two-dimensional signals are normally processed as rectangularly sampled arrays; i.e., they are periodically sampled in each of two orthogonal independent variables. Another form of periodic sampling, hexagonal sampling, offers substantial savings in machine storage and arithmetic computations for many signal processing operations. In this paper, methods for the processing of two-dimensional signals which have been sampled as two-dimensional hexagonal arrays are presented. Included are methods for signal representation, linear system implementation, frequency response calculation, DFT calculation, filter design, and filter implementation. These algorithms bear strong resemblances to the corresponding results for rectangular arrays; however, there are also many important differences. Some comparisons between the two methods for representing planar data will also be presented.

Lossy compression of noisy images

Noise degrades the performance of any image compression algorithm. This paper studies the effect of noise on lossy image compression. The effect of Gaussian, Poisson, and film-grain noise on compression is studied. To reduce the effect of the noise on compression, the distortion is measured with respect to the original image not to the input of the coder. Results of noisy source coding are then used to design the optimal coder. In the minimum-mean-square-error (MMSE) sense, this is equivalent to an MMSE estimator followed by an MMSE coder. The coders for the Poisson noise and the film-grain noise cases are derived and their performance is studied. The effect of this preprocessing step is studied using standard coders, e.g., JPEG, also. As is demonstrated, higher quality is achieved at lower bit rates.

Motion compensated compression of computer animation frames

This paper presents a new lossless compression algorithm for computer animation image sequences. The algorithm uses transformation information available in the animation script and floating point depth and object number information stored at each pixel to perform highly accurate motion prediction with very low computation. The geometric data, i.e., the depth and object number, is very efficiently compressed using motion prediction and a new technique called direction coding, typically to 1 to 2 bits per pixel. The geometric data is also useful in z-buffer image compositing and this new compression algorithm offers a very low storage overhead method for saving the information needed for z-buffer image compositing. The overall compression ratio of the new algorithm, including the geometric data overhead, is compared to conventional spatial linear prediction compression and is shown to be consistently better, by a factor of 1.4 or more, even with large frame-to-frame motion. CR Categories: I.4.2[compression(coding)]exact coding. Additional keywords: compression,computer animation,computer graphics, motion prediction

On increasing the convergence rate of regularized iterative image restoration algorithms

In [1] a regularized iterative algorithm was described which has been shown to be very suitable for solving the ill-posed image restoration problem. By incorporating deterministic constraints and adaptivity this very general algorithm is capable of achieving both noise suppression and ringing reduction in the restoration process. It consumes, however, considerable computation to obtain a (visually) stable solution due to the low convergence speed of the algorithm. The purpose of this paper is to investigate the possibilities for speeding up the convergence of this restoration method. To this end we compare the classical steepest descent algorithm (with linear convergence) with a conjugate gradients based method (superlinear convergence) and a new Q-th order converging algorithm. The latter solution method has the highest convergence rate, but is restricted in its application to space-invariant image restoration with a linear constraint. Although the actual convergence speed of the algorithms involved generally depends on the image data to be restored, it will be shown that for real-life images the constrained conjugate gradients algorithm yields a considerable convergence speed improvement.

Theory of paraunitary filter banks over fields of characteristic two

Motivated by our wavelet framework for error-control coding, we proceed to develop an important family of wavelet transforms over finite fields. Paraunitary (PU) filter banks that are realizations of orthogonal wavelets by multirate filters are an important subclass of perfect reconstruction (PR) filter banks. A parameterization of PU filter banks that covers all possible PU systems is very desirable in error-control coding because it provides a framework for optimizing the free parameters to maximize coding performance. This paper undertakes the problem of classifying all PU matrices with entries from a polynomial ring, where the coefficients of the polynomials are taken from finite fields. It constructs Householder transformations that are used as elementary operations for the realization of all unitary matrices. Then, it introduces elementary PU building blocks and a factorization technique that is specialized to obtain a complete realization for all PU filter banks over fields of characteristic two. This is proved for the 2 /spl times/ 2 case, and conjectured for the M /spl times/ M case, where M /spl ges/ 3. Using these elementary building blocks, we can construct all PU filter banks over fields of characteristic two. These filter banks can be used to implement transforms which, in turn, provide a powerful new perspective on the problems of constructing and decoding arbitrary-rate error-correcting codes.

Double Circulant Self-Dual Codes Using Finite-Field Wavelet Transforms

This paper presents an example of integrating recently developed finite-field wavelet transforms into the study of error correcting codes. The primary goal of the paper is to demonstrate a straightforward approach to analyzing double circulant self-dual codes over any arbitrary finite-field using orthogonal filter bank structures. First, we discuss the proper combining of the cyclic mother wavelet and scaling sequence to satisfy the requirement of self-dual codes. Then as an example, we describe the encoder and decoder of a (12,6,4) self-dual code, and we demonstrate the simplicity and the computation reduction that the wavelet method offers for the encoding and decoding of this code. Finally, we give the mother wavelet and scaling sequence that generate the (24,12,8) Golay code.

Lossless compression of computer generated animation frames

This article presents a new lossless compression algorithm for computer animation image sequences. The algorithm uses transformation information available in the animation script and floating point depth and object number information at each pixel to perform highly accurate motion prediction with vary low computation. The geometric data (i.e., the depth and object number) can either be computed during the original rendering process and stored with the image or computed on the fly during compression and decompression. In the former case the stored geometric data are very efficientlycomporessed using motion prediction and a new technique called direction coding, typically to 1 to 2 bits per pixel. The geometric data are also useful in z-buffer image compsiting and this new compression algorthm offers a very low storage overhead method for saving the information needed for this comoositing. The overall compression ratio of the new algorithm, including the geometic data overhead, in compared to conventional spatial linear prediction compression and block-matching motion. The algorithm improves on a previous motion prediction algorithm by incorporating block predictor switching and color ratio predition. The combination of thes techniques gives compression ratios 30% better than those reported previously.

An optimization of MPEG to maximize subjective quality

We present a video quality measure based on block-based features. Four block-based features (an average of FFT differences, a standard deviation of FFT differences, mean absolute deviation of wepstrum differences, and the variance of UVW differences) are extracted from the input and output video sequences and fed into a four-layer backpropagation neural network which has been trained by subjective testing. We then introduce the quality measure into the design of an MPEG encoder to maximize the quality measure. A MPEG bit allocation algorithm is developed which is based on the quality measure that considers the bit-count and quality at the macroblock level. A simple relationship between one macroblocks quality and overall quality is also addressed. The simulation on this optimization scheme has a higher quality measure when compared to the Test Model 5.

Realization of paraunitary filter banks over fields of characteristic two

Paraunitary filter banks are multi-rate filter realizations of orthogonal wavelet transforms. They are an important subclass of perfect reconstruction filter banks that provide a new framework for error control coding and decoding. This paper undertakes the problem of classifying all paraunitary matrices with entries from a polynomial ring, where the coefficients of the polynomials are taken from finite fields. It constructs Householder transformations that are used as elementary operations for the realization of all unitary matrices. Then, it introduces elementary paraunitary building blocks and a factorization technique that are specialized to obtain a complete realization for all paraunitary filter banks over fields of characteristic two (this is proved for the 2-band case, and a conjecture is applied for the proof of the M-band case, where M/spl ges/3). Using these elementary building blocks, we can construct all paraunitary filter banks over fields of characteristic two.