Aggelos K. Katsaggelos

Bio: Aggelos K. Katsaggelos is an academic researcher from Northwestern University. The author has contributed to research in topics: Image restoration & Image processing. The author has an hindex of 76, co-authored 946 publications receiving 26196 citations. Previous affiliations of Aggelos K. Katsaggelos include University of Stavanger & Delft University of Technology.

Digital Image Restoration

Abstract: The article introduces digital image restoration to the reader who is just beginning in this field, and provides a review and analysis for the reader who may already be well-versed in image restoration. The perspective on the topic is one that comes primarily from work done in the field of signal processing. Thus, many of the techniques and works cited relate to classical signal processing approaches to estimation theory, filtering, and numerical analysis. In particular, the emphasis is placed primarily on digital image restoration algorithms that grow out of an area known as "regularized least squares" methods. It should be noted, however, that digital image restoration is a very broad field, as we discuss, and thus contains many other successful approaches that have been developed from different perspectives, such as optics, astronomy, and medical imaging, just to name a few. In the process of reviewing this topic, we address a number of very important issues in this field that are not typically discussed in the technical literature.

Hybrid image segmentation using watersheds and fast region merging

Abstract: A hybrid multidimensional image segmentation algorithm is proposed, which combines edge and region-based techniques through the morphological algorithm of watersheds. An edge-preserving statistical noise reduction approach is used as a preprocessing stage in order to compute an accurate estimate of the image gradient. Then, an initial partitioning of the image into primitive regions is produced by applying the watershed transform on the image gradient magnitude. This initial segmentation is the input to a computationally efficient hierarchical (bottom-up) region merging process that produces the final segmentation. The latter process uses the region adjacency graph (RAG) representation of the image regions. At each step, the most similar pair of regions is determined (minimum cost RAG edge), the regions are merged and the RAG is updated. Traditionally, the above is implemented by storing all RAG edges in a priority queue. We propose a significantly faster algorithm, which additionally maintains the so-called nearest neighbor graph, due to which the priority queue size and processing time are drastically reduced. The final segmentation provides, due to the RAG, one-pixel wide, closed, and accurately localized contours/surfaces. Experimental results obtained with two-dimensional/three-dimensional (2-D/3-D) magnetic resonance images are presented.

Bayesian Compressive Sensing Using Laplace Priors

Abstract: In this paper, we model the components of the compressive sensing (CS) problem, i.e., the signal acquisition process, the unknown signal coefficients and the model parameters for the signal and noise using the Bayesian framework. We utilize a hierarchical form of the Laplace prior to model the sparsity of the unknown signal. We describe the relationship among a number of sparsity priors proposed in the literature, and show the advantages of the proposed model including its high degree of sparsity. Moreover, we show that some of the existing models are special cases of the proposed model. Using our model, we develop a constructive (greedy) algorithm designed for fast reconstruction useful in practical settings. Unlike most existing CS reconstruction methods, the proposed algorithm is fully automated, i.e., the unknown signal coefficients and all necessary parameters are estimated solely from the observation, and, therefore, no user-intervention is needed. Additionally, the proposed algorithm provides estimates of the uncertainty of the reconstructions. We provide experimental results with synthetic 1-D signals and images, and compare with the state-of-the-art CS reconstruction algorithms demonstrating the superior performance of the proposed approach.

Error resilient video coding techniques

Abstract: We review error resilience techniques for real-time video transport over unreliable networks. Topics covered include an introduction to today's protocol and network environments and their characteristics, encoder error resilience tools, decoder error concealment techniques, as well as techniques that require cooperation between encoder, decoder, and the network. We provide a review of general principles of these techniques as well as specific implementations adopted by the H.263 and MPEG-4 video coding standards. The majority of the article is devoted to the techniques developed for block-based hybrid coders using motion-compensated prediction and transform coding. A separate section covers error resilience techniques for shape coding in MPEG-4.

Methods for choosing the regularization parameter and estimating the noise variance in image restoration and their relation

Abstract: The application of regularization to ill-conditioned problems necessitates the choice of a regularization parameter which trades fidelity to the data with smoothness of the solution. The value of the regularization parameter depends on the variance of the noise in the data. The problem of choosing the regularization parameter and estimating the noise variance in image restoration is examined. An error analysis based on an objective mean-square-error (MSE) criterion is used to motivate regularization. Two approaches for choosing the regularization parameter and estimating the noise variance are proposed. The proposed and existing methods are compared and their relationship to linear minimum-mean-square-error filtering is examined. Experiments are presented that verify the theoretical results. >

I and i

Abstract: There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality. Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

Pattern Recognition and Machine Learning

Abstract: Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Image Super-Resolution Using Deep Convolutional Networks

Abstract: We propose a deep learning method for single image super-resolution (SR). Our method directly learns an end-to-end mapping between the low/high-resolution images. The mapping is represented as a deep convolutional neural network (CNN) that takes the low-resolution image as the input and outputs the high-resolution one. We further show that traditional sparse-coding-based SR methods can also be viewed as a deep convolutional network. But unlike traditional methods that handle each component separately, our method jointly optimizes all layers. Our deep CNN has a lightweight structure, yet demonstrates state-of-the-art restoration quality, and achieves fast speed for practical on-line usage. We explore different network structures and parameter settings to achieve trade-offs between performance and speed. Moreover, we extend our network to cope with three color channels simultaneously, and show better overall reconstruction quality.