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Research on this contract was directed towards areas of mathematics and numerical computation which have applications to image/signal processing. The research can be broadly classified into the following areas: (i) image processing, (ii) processing digital terrain data, (iii) wavelets and multi resolution, (iv) information theory, (v) analogue to digital signal conversion, and (vi) approximation. The highlights of the scientific accomplishments include: development of compression methods for Digital Terrain Elevation Data, solution of external problems for image denoising using wavelets, construction of new wavelet bases, development of high order methods for conversion between analogue and digital signals.

The transmission properties of some bacteriorhodopsin-film spatial light modulators are uniquely suited to allow nonlinear optical image-processing operations to be applied to images with multiplicative noise characteristics. A logarithmic amplitude-transmission characteristic of the film permits the conversion of multiplicative noise to additive noise, which may then be linearly filtered out in the Fourier plane of the transformed image. I present experimental results demonstrating the principle and the capability for several different image and noise situations, including deterministic noise and speckle. The bacteriorhodopsin film studied here displays the logarithmic transmission response for write intensities spanning a dynamic range greater than 2 orders of magnitude.

The transmission properties of some bacteriorhodopsin-film spatial light modulators are uniquely suited to allow nonlinear optical image-processing operations to be applied to images with multiplicative noise characteristics. A logarithmic amplitude-transmission characteristic of the film permits the conversion of multiplicative noise to additive noise, which may then be linearly filtered out in the Fourier plane of the transformed image. I present experimental results demonstrating the principle and the capability for several different image and noise situations, including deterministic noise and speckle. The bacteriorhodopsin film studied here displays the logarithmic transmission response for write intensities spanning a dynamic range greater than 2 orders of magnitude.

The transmission properties of some bacteriorhodopsin-film spatial light modulators are uniquely suited to allow nonlinear optical image-processing operations to be applied to images with multiplicative noise characteristics. A logarithmic amplitude-transmission characteristic of the film permits the conversion of multiplicative noise to additive noise, which may then be linearly filtered out in the Fourier plane of the transformed image. I present experimental results demonstrating the principle and the capability for several different image and noise situations, including deterministic noise and speckle. The bacteriorhodopsin film studied here displays the logarithmic transmission response for write intensities spanning a dynamic range greater than 2 orders of magnitude.

In this paper the use of nonlinear cross-diffu\-sion systems to model image restoration is investigated, theoretically and numerically. In the first case, well-posedness, scale-space properties and long time behaviour are analyzed. From a numerical point of view, a computational study of the performance of the models is carried out, suggesting their diversity and potentialities to treat image filtering problems. The present paper is a continuation of a previous work of the same authors, devoted to linear cross-diffusion models. \keywords{Cross-diffusion \and Complex diffusion \and Image restoration}

This project included basic studies of infrared nonlinear optical response and optical switching in semiconductor materials. Investigations ranged from the mid-infrared (InAs) through the 1.06 micron region (InP/based quaternaries) to the near-IR (GaAs/GaAlAs Multiple Quantum Wells). Mechanisms of dynamic state filling were explored; the stdy was extended to exciton resonance nonlinearities and finally the concept of enhanced carrier transport nonlinearities was introduced. This new non-local nonlinearity is due to the motion of optically induced charges within semiconductor depletion regions causing space change fields which decrease built-in fields. The optically induced change in internal fields causes nonlinear transmission due to electro- absorption, electro-refraction, and the quantum confined Stark effect. The result was the experimental demonstration of larger nonlinearities than have ever been previously measured, with a change of refractive index of 0.01 at an intensity level of 700 microwatts/sq cm.

This project included basic studies of infrared nonlinear optical response and optical switching in semiconductor materials. Investigations ranged from the mid-infrared (InAs) through the 1.06 micron region (InP/based quaternaries) to the near-IR (GaAs/GaAlAs Multiple Quantum Wells). Mechanisms of dynamic state filling were explored; the stdy was extended to exciton resonance nonlinearities and finally the concept of enhanced carrier transport nonlinearities was introduced. This new non-local nonlinearity is due to the motion of optically induced charges within semiconductor depletion regions causing space change fields which decrease built-in fields. The optically induced change in internal fields causes nonlinear transmission due to electro- absorption, electro-refraction, and the quantum confined Stark effect. The result was the experimental demonstration of larger nonlinearities than have ever been previously measured, with a change of refractive index of 0.01 at an intensity level of 700 microwatts/sq cm.

A range of nonlinear image reconstruction procedures based on extremizing the generalized Shannon entropy, Kullback-Leibler cross-entropy and Renyi information measures and proposed by the author in early papers is presented. The ``generalization'' assumes search for the solution over the space of real bipolar or complex functions. Such an approach allows, first, to reconstruct signals of any type and physical nature and, secondly, to decrease nonlinear intensity image distortions caused by measurement errors. All the elaborated procedures are contained in VLBI ``IMAGE'' program package developed in IAA RAS.

A range of nonlinear image reconstruction procedures based on extremizing the generalized Shannon entropy, Kullback-Leibler cross-entropy and Renyi information measures and proposed by the author in early papers is presented. The ``generalization'' assumes search for the solution over the space of real bipolar or complex functions. Such an approach allows, first, to reconstruct signals of any type and physical nature and, secondly, to decrease nonlinear intensity image distortions caused by measurement errors. All the elaborated procedures are contained in VLBI ``IMAGE'' program package developed in IAA RAS.

For as long as periodically poled devices have been produced, there has been a need to evaluate and improve their performance. A new approach based on image processing across an entire z+ or z- surface of a poled crystal allows for better quantification of the underlying domain structure and directly relates to device performance. The poled regions are determined from the images and this mapping is then used to determine an effective nonlinear d-coefficient. Experimentally validated measurements are shown for an optical parametric generator setup. Future improvements in the poling process should be possible by using this technique to produce quantifiable metrics to compare device fabrication iterations, which has applications in Quality Assurance as well as device development.

Data representation, which is often overlooked in many image processing and analysis applications, is as critical as the algorithms applied to that data. When data is represented properly, simple algorithms can be much more powerful than sophisticated and often complex algorithms applied to an improper representation. In an image, the useful information is generally mixed in with irrelevant information or noise and often it is difficult for the computer to separate the useful information from the large volume of irrelevant data without destroying much of the useful data. To provide a solid foundation for a good solution to this problem, multiresolution decomposition and synthesis approaches have been developed which decompose raw image data into a set of partial information channels, where each channel represents a certain modality (or aspect) of the raw image. The channels can then be processed individually or cooperatively with a wide variety of results possible.

Existence and uniqueness are established for a degenerate regularization of the well-known Perona-Malik equation proposed by the first author for non-smooth initial data. The results heavily rely on the choice of appropriate functional setting inspired by a recent approach to degenerate parabolic equations via so-called singular Riemannian manifolds introduced by Herbert Amann.

THis work is a survey of a few nonlinear PDE based models in image restoring.

The transmission properties of some bacteriorhodopsin-film spatial light modulators are uniquely suited to allow nonlinear optical image-processing operations to be applied to images with multiplicative noise characteristics. A logarithmic amplitude-transmission characteristic of the film permits the conversion of multiplicative noise to additive noise, which may then be linearly filtered out in the Fourier plane of the transformed image. I present experimental results demonstrating the principle and the capability for several different image and noise situations, including deterministic noise and speckle. The bacteriorhodopsin film studied here displays the logarithmic transmission response for write intensities spanning a dynamic range greater than 2 orders of magnitude.

The transmission properties of some bacteriorhodopsin-film spatial light modulators are uniquely suited to allow nonlinear optical image-processing operations to be applied to images with multiplicative noise characteristics. A logarithmic amplitude-transmission characteristic of the film permits the conversion of multiplicative noise to additive noise, which may then be linearly filtered out in the Fourier plane of the transformed image. I present experimental results demonstrating the principle and the capability for several different image and noise situations, including deterministic noise and speckle. The bacteriorhodopsin film studied here displays the logarithmic transmission response for write intensities spanning a dynamic range greater than 2 orders of magnitude.

The transmission properties of some bacteriorhodopsin-film spatial light modulators are uniquely suited to allow nonlinear optical image-processing operations to be applied to images with multiplicative noise characteristics. A logarithmic amplitude-transmission characteristic of the film permits the conversion of multiplicative noise to additive noise, which may then be linearly filtered out in the Fourier plane of the transformed image. I present experimental results demonstrating the principle and the capability for several different image and noise situations, including deterministic noise and speckle. The bacteriorhodopsin film studied here displays the logarithmic transmission response for write intensities spanning a dynamic range greater than 2 orders of magnitude.

Abstract -Tlds is a pictorial survey of pattern dynamics in video feed­back and in related numerical models. After a short introduction to video feedback apparatus and concepts from dynamcal systems theory, a range of phenomena are presented, from simple ...