Convexity in source separation: Models, geometry, and algorithms

Source separation or demixing is the process of extracting multiple components entangled within a signal. Contemporary signal processing presents a host of difficult source separation problems, from interference cancellation to background subtraction, blind deconvolution, and even dictionary learning. Despite the recent progress in each of these applications, advances in high-throughput sensor technology place demixing algorithms under pressure to accommodate extremely high-dimensional signals, separate an ever larger number of sources, and cope with more sophisticated signal and mixing models. These difficulties are exacerbated by the need for real-time action in automated decision-making systems. Recent advances in convex optimization provide a simple framework for efficiently solving numerous difficult demixing problems. This article provides an overview of the emerging field, explains the theory that governs the underlying procedures, and surveys algorithms that solve them efficiently. We aim to equip practitioners with a toolkit for constructing their own demixing algorithms that work, as well as concrete intuition for why they work

RIBBONS: Rapid Inpainting Based on Browsing of Neighborhood Statistics

Image inpainting refers to filling missing places in images using neighboring pixels. It also has many applications in different tasks of image processing. Most of these applications enhance the image quality by significant unwanted changes or even elimination of some existing pixels. These changes require considerable computational complexities which in turn results in remarkable processing time. In this paper we propose a fast inpainting algorithm called RIBBONS based on selection of patches around each missing pixel. This would accelerate the execution speed and the capability of online frame inpainting in video. The applied cost-function is a combination of statistical and spatial features in all neighboring pixels. We evaluate some candidate patches using the proposed cost function and minimize it to achieve the final patch. Experimental results show the higher speed of 'Ribbons' in comparison with previous methods while being comparable in terms of PSNR and SSIM for the images in MISC dataset

Data-Driven Shape Analysis and Processing

Data-driven methods play an increasingly important role in discovering geometric, structural, and semantic relationships between 3D shapes in collections, and applying this analysis to support intelligent modeling, editing, and visualization of geometric data. In contrast to traditional approaches, a key feature of data-driven approaches is that they aggregate information from a collection of shapes to improve the analysis and processing of individual shapes. In addition, they are able to learn models that reason about properties and relationships of shapes without relying on hard-coded rules or explicitly programmed instructions. We provide an overview of the main concepts and components of these techniques, and discuss their application to shape classification, segmentation, matching, reconstruction, modeling and exploration, as well as scene analysis and synthesis, through reviewing the literature and relating the existing works with both qualitative and numerical comparisons. We conclude our report with ideas that can inspire future research in data-driven shape analysis and processing.Comment: 10 pages, 19 figure