X-ray image separation via coupled dictionary learning

In support of art investigation, we propose a new source sepa- ration method that unmixes a single X-ray scan acquired from double-sided paintings. Unlike prior source separation meth- ods, which are based on statistical or structural incoherence of the sources, we use visual images taken from the front- and back-side of the panel to drive the separation process. The coupling of the two imaging modalities is achieved via a new multi-scale dictionary learning method. Experimental results demonstrate that our method succeeds in the discrimination of the sources, while state-of-the-art methods fail to do so.Comment: To be presented at the IEEE International Conference on Image Processing (ICIP), 201

Multi-modal dictionary learning for image separation with application in art investigation

In support of art investigation, we propose a new source separation method that unmixes a single X-ray scan acquired from double-sided paintings. In this problem, the X-ray signals to be separated have similar morphological characteristics, which brings previous source separation methods to their limits. Our solution is to use photographs taken from the front and back-side of the panel to drive the separation process. The crux of our approach relies on the coupling of the two imaging modalities (photographs and X-rays) using a novel coupled dictionary learning framework able to capture both common and disparate features across the modalities using parsimonious representations; the common component models features shared by the multi-modal images, whereas the innovation component captures modality-specific information. As such, our model enables the formulation of appropriately regularized convex optimization procedures that lead to the accurate separation of the X-rays. Our dictionary learning framework can be tailored both to a single- and a multi-scale framework, with the latter leading to a significant performance improvement. Moreover, to improve further on the visual quality of the separated images, we propose to train coupled dictionaries that ignore certain parts of the painting corresponding to craquelure. Experimentation on synthetic and real data - taken from digital acquisition of the Ghent Altarpiece (1432) - confirms the superiority of our method against the state-of-the-art morphological component analysis technique that uses either fixed or trained dictionaries to perform image separation.Comment: submitted to IEEE Transactions on Images Processin

Wavelets and wavelet-like transforms on the sphere and their application to geophysical data inversion

Many flexible parameterizations exist to represent data on the sphere. In addition to the venerable spherical harmonics, we have the Slepian basis, harmonic splines, wavelets and wavelet-like Slepian frames. In this paper we focus on the latter two: spherical wavelets developed for geophysical applications on the cubed sphere, and the Slepian "tree", a new construction that combines a quadratic concentration measure with wavelet-like multiresolution. We discuss the basic features of these mathematical tools, and illustrate their applicability in parameterizing large-scale global geophysical (inverse) problems.Comment: 15 pages, 11 figures, submitted to the Proceedings of the SPIE 2011 conference Wavelets and Sparsity XI

Application of wavelets to singular integral scattering equations

The use of orthonormal wavelet basis functions for solving singular integral scattering equations is investigated. It is shown that these basis functions lead to sparse matrix equations which can be solved by iterative techniques. The scaling properties of wavelets are used to derive an efficient method for evaluating the singular integrals. The accuracy and efficiency of the wavelet transforms is demonstrated by solving the two-body T-matrix equation without partial wave projection. The resulting matrix equation which is characteristic of multiparticle integral scattering equations is found to provide an efficient method for obtaining accurate approximate solutions to the integral equation. These results indicate that wavelet transforms may provide a useful tool for studying few-body systems.Comment: 11 pages, 4 figure

Accelerated Projected Gradient Method for Linear Inverse Problems with Sparsity Constraints

Regularization of ill-posed linear inverse problems via $\ell_1$ penalization has been proposed for cases where the solution is known to be (almost) sparse. One way to obtain the minimizer of such an $\ell_1$ penalized functional is via an iterative soft-thresholding algorithm. We propose an alternative implementation to $\ell_1$-constraints, using a gradient method, with projection on $\ell_1$-balls. The corresponding algorithm uses again iterative soft-thresholding, now with a variable thresholding parameter. We also propose accelerated versions of this iterative method, using ingredients of the (linear) steepest descent method. We prove convergence in norm for one of these projected gradient methods, without and with acceleration.Comment: 24 pages, 5 figures. v2: added reference, some amendments, 27 page

USO DE RECEPTORES GPS DE 100 HZ NA DETECÇÃO DE DEFLEXÕES VERTICAIS MILIMÉTRICAS DE PONTES DE CONCRETO DE PEQUENO PORTE

As últimas quatro décadas foram importantes para o desenvolvimento da malha rodoviária brasileira. O país recebeu incentivos financeiros para a sua expansão e diversas soluções estruturais para pontes e viadutos foram criadas. Em paralelo a este desenvolvimento, houve nos últimos anos um crescimento significativo dessas estruturas em estágio avançado de deterioração devido à ausência de programas de manutenção preventiva. Dessa maneira, este trabalho propõe o uso de receptores GPS num plano de monitoramento de curta duração para acompanhar o comportamento estrutural de uma ponte rodoviária curva de concreto armado já em serviço. E apresenta os primeiros resultados da pesquisa com a portadora L1 do sistema GPS e dados gravados com taxa de 100 Hz, no monitoramento do vão central de ponte de concreto de pequeno porte situada sobre o Rio Jaguari, na cidade de Extrema, divisa entre os Estados de Minas Gerais e São Paulo. O desafio reside no fato de que estruturas como estas - pontes de concreto de pequeno e médio porte - respondem pela grande maioria das obras de arte da malha rodoviária brasileira e por serem estruturas rígidas, apresentam deflexões verticais pequenas, de até 5mm. O experimento foi realizado por meio de sessões de observações com receptores GPS sobre a ponte, no vão instrumentado por equipamentos convencionais para posterior confrontação de resultados entre os receptores GPS e os métodos clássicos de monitoramento. A ferramenta de filtragem Continuos Wavelet Transform (CWT) foi utilizada para analisar as frequências de resposta da ponte a partir dos resíduos da dupla diferença de fase da portadora L1. A análise do espectro de energia da CWT gerado a partir dos dados coletados com os receptores GPS indicou alta concentração de energia nas mesmas faixas de frequência - de resposta do tabuleiro da ponte - apontadas pela Modelagem por Elementos Finitos e pela prova de carga dinâmica