3rd Workshop in Symbolic Data Analysis: book of abstracts

This workshop is the third regular meeting of researchers interested in Symbolic Data Analysis. The main aim of the event is to favor the meeting of people and the exchange of ideas from different fields - Mathematics, Statistics, Computer Science, Engineering, Economics, among others - that contribute to Symbolic Data Analysis

Subspace averaging and order determination for source enumeration

In this paper, we address the problem of subspace averaging, with special emphasis placed on the question of estimating the dimension of the average. The results suggest that the enumeration of sources in a multi-sensor array, which is a problem of estimating the dimension of the array manifold, and as a consequence the number of radiating sources, may be cast as a problem of averaging subspaces. This point of view stands in contrast to conventional approaches, which cast the problem as one of identifiying covariance models in a factor model. We present a robust formulation of the proposed order fitting rule based on majorization-minimization algorithms. A key element of the proposed method is to construct a bootstrap procedure, based on a newly proposed discrete distribution on the manifold of projection matrices, for stochastically generating subspaces from a function of experimentally determined eigenvalues. In this way, the proposed subspace averaging (SA) technique determines the order based on the eigenvalues of an average projection matrix, rather than on the likelihood of a covariance model, penalized by functions of the model order. By means of simulation examples, we show that the proposed SA criterion is especially effective in high-dimensional scenarios with low sample support.The associate editor coordinating the review of this manuscript and approving it for publication was Prof. Yuejie Chi. The work of V. Garg and I. Santamaria was supported in part by the Ministerio de Economía y Competitividad (MINECO) of Spain, and in part by the AEI/FEDER funds of the E.U., under Grants TEC2016-75067-C4-4-R (CARMEN), TEC2015-69648-REDC, and BES-2017-080542. The work of D. Ramírez was supported in part by the Ministerio de Ciencia, Innovación y Universidades under Grant TEC2017-92552-EXP (aMBITION), in part by the Ministerio de Ciencia, Innovación y Universidades, jointly with the European Commission (ERDF), under Grants TEC2015-69868-C2-1-R (ADVENTURE) and TEC2017-86921-C2-2-R (CAIMAN), and in part by The Comunidad de Madrid under Grant Y2018/TCS-4705 (PRACTICOCM). The work of L. L. Scharf was supported in part by the U.S. NSF under Contract CISE-1712788

Recent Progress in Image Deblurring

This paper comprehensively reviews the recent development of image deblurring, including non-blind/blind, spatially invariant/variant deblurring techniques. Indeed, these techniques share the same objective of inferring a latent sharp image from one or several corresponding blurry images, while the blind deblurring techniques are also required to derive an accurate blur kernel. Considering the critical role of image restoration in modern imaging systems to provide high-quality images under complex environments such as motion, undesirable lighting conditions, and imperfect system components, image deblurring has attracted growing attention in recent years. From the viewpoint of how to handle the ill-posedness which is a crucial issue in deblurring tasks, existing methods can be grouped into five categories: Bayesian inference framework, variational methods, sparse representation-based methods, homography-based modeling, and region-based methods. In spite of achieving a certain level of development, image deblurring, especially the blind case, is limited in its success by complex application conditions which make the blur kernel hard to obtain and be spatially variant. We provide a holistic understanding and deep insight into image deblurring in this review. An analysis of the empirical evidence for representative methods, practical issues, as well as a discussion of promising future directions are also presented.Comment: 53 pages, 17 figure