Solving a variational image restoration model which involves L∞ constraints

In this paper, we seek a solution to linear inverse problems arising in image restoration in terms of a recently posed optimization problem which combines total variation minimization and wavelet-thresholding ideas. The resulting nonlinear programming task is solved via a dual Uzawa method in its general form, leading to an efficient and general algorithm which allows for very good structure-preserving reconstructions. Along with a theoretical study of the algorithm, the paper details some aspects of the implementation, discusses the numerical convergence and eventually displays a few images obtained for some difficult restoration tasks

Guided Nonlocal Patch Regularization and Efficient Filtering-Based Inversion for Multiband Fusion

In multiband fusion, an image with a high spatial and low spectral resolution is combined with an image with a low spatial but high spectral resolution to produce a single multiband image having high spatial and spectral resolutions. This comes up in remote sensing applications such as pansharpening~(MS+PAN), hyperspectral sharpening~(HS+PAN), and HS-MS fusion~(HS+MS). Remote sensing images are textured and have repetitive structures. Motivated by nonlocal patch-based methods for image restoration, we propose a convex regularizer that (i) takes into account long-distance correlations, (ii) penalizes patch variation, which is more effective than pixel variation for capturing texture information, and (iii) uses the higher spatial resolution image as a guide image for weight computation. We come up with an efficient ADMM algorithm for optimizing the regularizer along with a standard least-squares loss function derived from the imaging model. The novelty of our algorithm is that by expressing patch variation as filtering operations and by judiciously splitting the original variables and introducing latent variables, we are able to solve the ADMM subproblems efficiently using FFT-based convolution and soft-thresholding. As far as the reconstruction quality is concerned, our method is shown to outperform state-of-the-art variational and deep learning techniques.Comment: Accepted in IEEE Transactions on Computational Imagin

Study of Target Enhancement Algorithms to Counter the Hostile Nuclear Environment

A necessary requirement of strategic defense is the detection of incoming nuclear warheads in an environment that may include nuclear detonations of undetected or missed target warheads. A computer model is described which simulates incoming warheads as distant endoatmospheric targets. A model of the expected electromagnetic noise present in a nuclear environment is developed using estimates of the probability distributions. Predicted atmospheric effects are also included. Various image enhancement algorithms, both linear and nonlinear, are discussed concerning their anticipated ability to suppress the noise and atmospheric effects of the nuclear environment. These algorithms are then tested, using the combined target and noise models, and evaluated in terms of the stated figures of merit

Representations for Morphological Image Operators and Analogies with Linear Operators

1.1 Why a representation theory?...............................

Generalized filtering configurations with applications in digital and optical signal and image processing

Ankara : Department of Electrical and Electonics Engineering and Institute of Engineering and Sciences, Bilkent Univ., 1999.Thesis (Ph.D.) -- Bilkent University, 1999.Includes bibliographical refences.In this thesis, we first give a brief summary of the fractional Fourier transform which is the generalization of the ordinary Fourier transform, discuss its importance in optical and digital signal processing and its relation to time-frequency representations. We then introduce the concept of filtering circuits in fractional Fourier domains. This concept unifies the multi-stage (repeated) and multi-channel (parallel) filtering configurations which are in turn generalizations of single domain filtering in fractional Fourier domains. We show that these filtering configurations allow a cost-accuracy tradeoff by adjusting the number of stages or channels. We then consider the application of these configurations to three important problems, namely system synthesis, signal synthesis, and signal recovery, in optical and digital signal processing. In the system and signal synthesis problems, we try to synthesize a desired system characterized by its kernel, or a desired signal characterized by its second order statistics by using fractional Fourier domain filtering circuits. In the signal recovery problem, we try to recover or estimate a desired signal from its degraded version. In all of the examples we give, significant improvements in performance are obtained with respect to single domain filtering methods with only modest increases in optical or digital implementation costs. Similarly, when the proposed method is compared with the direct implementation of general linear systems, we see that significant computational savings are obtained with acceptable decreases in performance.Kutay, Mehmet AlperPh.D