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 wavelet based numerical method for nonlinear partial differential equations

The purpose of this paper is to present a wavelet–Galerkin scheme for solving nonlinear elliptic partial differential equations. We select as trial spaces a nested sequence of spaces from an appropriate biorthogonal multiscale analysis. This gives rise to a nonlinear discretized system. To overcome the problems of nonlinearity, we apply the machinery of interpolating wavelets to obtain knot oriented quadrature rules. Finally, Newton’s method is applied to approximate the solution in the given ansatz space. The results of some numerical experiments with different biorthogonal systems, confirming the applicability of our scheme, are presented.Instituto de Cooperação Científica e Tecnológica Internacional - Acções Integradas Luso-Alemãs (DAAD/ICCTI) - Projecto DAAD/ICCTI nº 01141

Dielectric exchange-force effect on the rupture force of adsorbed bilayers of self-assembled surfactant films

We measured and formulated dielectric exchange forces between adsorbed layers of self-assembled surfactant films and atomic-force microscope tips in water. The dielectric exchange-force model is in agreement with the observation that the surfactant-layer rupture forces (tip-applied force necessary to obtain tip/substrate contact) are smaller in the thickest layers, where the compactness of the adsorbed film results in the smallest values of the dielectric permittivity. Within experimental accuracy, a dielectric permittivity value of similar to4 for bilayers and of similar to 36 for monolayers is found. (C) 2001 American Institute of Physics.78203064306

Imaging of soft structures: Dependence of contrast in atomic force microscopy images on the force applied by the tip

Forces acting on atomic force microscope tips during scanning of films of ionic surfactant molecules adsorbed from aqueous solutions onto hydrophilic substrates are measured. Near critical micellar concentration images of mica substrates show aggregate regions at the interface. Force versus distance curves indicate that aggregates are the thickest adsorbed structures on the substrate. However, topographic images registered at low scanning speed (15 mu m/s) show that these aggregates appear as holes, consequently observed as inverted in contrast images, Tn atomic force microscope imaging of soft structures such as surfactants or biological material, inverted images may be observed when the tip penetrates the scanned layers. This penetration can be adjusted by changing the force applied by the tip, which results in different images. In order to obtain the conventional atomic force microscope contrast in scanned images the applied force set point is determined by the analysis of the force versus distance curves. (C) 2000 American Vacuum Society. [S0734-211X(00)11803-7].1831144115

Interfacial water dielectric-permittivity-profile measurements using atomic force microscopy

The arrangement of water molecules at charged aqueous interfaces is an important question in biology, electrochemistry, and geochemistry. Theoretical studies suggest that the molecules become arranged in several layers adjacent to a solid interface. Using atomic force microscopy we have measured the water dielectric-permittivity profile perpendicular to mica surfaces. The measured variable permittivity profile starting at epsilon approximate to4 at the interface and increasing to epsilon =80 about 10 nm from the surface suggests a reorientation of water molecule dipoles in the presence of the mica interfacial charge.641

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