Variational image restoration by means of wavelets: Simultaneous decomposition, deblurring, and denoising

AbstractInspired by papers of Vese–Osher [Modeling textures with total variation minimization and oscillating patterns in image processing, Technical Report 02-19, 2002] and Osher–Solé–Vese [Image decomposition and restoration using total variation minimization and the H−1 norm, Technical Report 02-57, 2002] we present a wavelet-based treatment of variational problems arising in the field of image processing. In particular, we follow their approach and discuss a special class of variational functionals that induce a decomposition of images into oscillating and cartoon components and possibly an appropriate ‘noise’ component. In the setting of [Modeling textures with total variation minimization and oscillating patterns in image processing, Technical Report 02-19, 2002] and [Image decomposition and restoration using total variation minimization and the H−1 norm, Technical Report 02-57, 2002], the cartoon component of an image is modeled by a BV function; the corresponding incorporation of BV penalty terms in the variational functional leads to PDE schemes that are numerically intensive. By replacing the BV penalty term by a B11(L1) term (which amounts to a slightly stronger constraint on the minimizer), and writing the problem in a wavelet framework, we obtain elegant and numerically efficient schemes with results very similar to those obtained in [Modeling textures with total variation minimization and oscillating patterns in image processing, Technical Report 02-19, 2002] and [Image decomposition and restoration using total variation minimization and the H−1 norm, Technical Report 02-57, 2002]. This approach allows us, moreover, to incorporate general bounded linear blur operators into the problem so that the minimization leads to a simultaneous decomposition, deblurring and denoising

A common and unstable copy number variant is associated with differences in Glo1 expression and anxiety-like behavior

Glyoxalase 1 (Glo1) has been implicated in anxiety-like behavior in mice and in multiple psychiatric diseases in humans. We used mouse Affymetrix exon arrays to detect copy number variants (CNV) among inbred mouse strains and thereby identified a approximately 475 kb tandem duplication on chromosome 17 that includes Glo1 (30,174,390-30,651,226 Mb; mouse genome build 36). We developed a PCR-based strategy and used it to detect this duplication in 23 of 71 inbred strains tested, and in various outbred and wild-caught mice. Presence of the duplication is associated with a cis-acting expression QTL for Glo1 (LOD>30) in BXD recombinant inbred strains. However, evidence for an eQTL for Glo1 was not obtained when we analyzed single SNPs or 3-SNP haplotypes in a panel of 27 inbred strains. We conclude that association analysis in the inbred strain panel failed to detect an eQTL because the duplication was present on multiple highly divergent haplotypes. Furthermore, we suggest that non-allelic homologous recombination has led to multiple reversions to the non-duplicated state among inbred strains. We show associations between multiple duplication-containing haplotypes, Glo1 expression and anxiety-like behavior in both inbred strain panels and outbred CD-1 mice. Our findings provide a molecular basis for differential expression of Glo1 and further implicate Glo1 in anxiety-like behavior. More broadly, these results identify problems with commonly employed tests for association in inbred strains when CNVs are present. Finally, these data provide an example of biologically significant phenotypic variability in model organisms that can be attributed to CNVs.These studies were funded by MH070933, MH79103 and MH020065

House mouse colonization patterns on the sub-Antarctic Kerguelen Archipelago suggest singular primary invasions and resilience against re-invasion

Starting from Western Europe, the house mouse (Mus musculus domesticus) has spread across the globe in historic times. However, most oceanic islands were colonized by mice only within the past 300 years. This makes them an excellent model for studying the evolutionary processes during early stages of new colonization. We have focused here on the Kerguelen Archipelago, located within the sub-Antarctic area and compare the patterns with samples from other Southern Ocean islands

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

Did tool-use evolve with enhanced physical cognitive abilities?

The use and manufacture of tools have been considered to be cognitively demanding and thus a possible driving factor in the evolution of intelligence. In this study, we tested the hypothesis that enhanced physical cognitive abilities evolved in conjunction with the use of tools, by comparing the performance of naturally tool-using and non-tool-using species in a suite of physical and general learning tasks. We predicted that the habitually tool-using species, New Caledonian crows and Galápagos woodpecker finches, should outperform their non-tool-using relatives, the small tree finches and the carrion crows in a physical problem but not in general learning tasks. We only found a divergence in the predicted direction for corvids. That only one of our comparisons supports the predictions under this hypothesis might be attributable to different complexities of tool-use in the two tool-using species. A critical evaluation is offered of the conceptual and methodological problems inherent in comparative studies on tool-related cognitive abilities

Mortality from lung cancer in workers exposed to sulfur dioxide in the pulp and paper industry.

Our objective in this study was to evaluate the mortality of workers exposed to sulfur dioxide in the pulp and paper industry. The cohort included 57,613 workers employed for at least 1 year in the pulp and paper industry in 12 countries. We assessed exposure to SO(2) at the level of mill and department, using industrial hygiene measurement data and information from company questionnaires; 40,704 workers were classified as exposed to SO(2). We conducted a standardized mortality ratio (SMR) analysis based on age-specific and calendar period-specific national mortality rates. We also conducted a Poisson regression analysis to determine the dose-response relations between SO(2) exposure and cancer mortality risks and to explore the effect of potential confounding factors. The SMR analysis showed a moderate deficit of all causes of death [SMR = 0.89; 95% confidence interval (CI), 0.87-0.96] among exposed workers. Lung cancer mortality was marginally increased among exposed workers (SMR = 1.08; 95% CI, 0.98-1.18). After adjustment for occupational coexposures, the lung cancer risk was increased compared with unexposed workers (rate ratio = 1.49; 95% CI, 1.14-1.96). There was a suggestion of a positive relationship between weighted cumulative SO(2) exposure and lung cancer mortality (p-value of test for linear trend = 0.009 among all exposed workers; p = 0.3 among workers with high exposure). Neither duration of exposure nor time since first exposure was associated with lung cancer mortality. Mortality from non-Hodgkin lymphoma and from leukemia was increased among workers with high SO(2) exposure; a dose-response relationship with cumulative SO(2) exposure was suggested for non-Hodgkin lymphoma. For the other causes of death, there was no evidence of increased mortality associated with exposure to SO(2). Although residual confounding may have occurred, our results suggest that occupational exposure to SO(2) in the pulp and paper industry may be associated with an increased risk of lung cancer