Direct 3D Tomographic Reconstruction and Phase-Retrieval of Far-Field Coherent Diffraction Patterns

We present an alternative numerical reconstruction algorithm for direct tomographic reconstruction of a sample refractive indices from the measured intensities of its far-field coherent diffraction patterns. We formulate the well-known phase-retrieval problem in ptychography in a tomographic framework which allows for simultaneous reconstruction of the illumination function and the sample refractive indices in three dimensions. Our iterative reconstruction algorithm is based on the Levenberg-Marquardt algorithm. We demonstrate the performance of our proposed method with simulation studies

A Convex Reconstruction Model for X-ray Tomographic Imaging with Uncertain Flat-fields

Classical methods for X-ray computed tomography are based on the assumption that the X-ray source intensity is known, but in practice, the intensity is measured and hence uncertain. Under normal operating conditions, when the exposure time is sufficiently high, this kind of uncertainty typically has a negligible effect on the reconstruction quality. However, in time- or dose-limited applications such as dynamic CT, this uncertainty may cause severe and systematic artifacts known as ring artifacts. By carefully modeling the measurement process and by taking uncertainties into account, we derive a new convex model that leads to improved reconstructions despite poor quality measurements. We demonstrate the effectiveness of the methodology based on simulated and real data sets.Comment: Accepted at IEEE Transactions on Computational Imagin

Decomposition in conic optimization with partially separable structure

Decomposition techniques for linear programming are difficult to extend to conic optimization problems with general non-polyhedral convex cones because the conic inequalities introduce an additional nonlinear coupling between the variables. However in many applications the convex cones have a partially separable structure that allows them to be characterized in terms of simpler lower-dimensional cones. The most important example is sparse semidefinite programming with a chordal sparsity pattern. Here partial separability derives from the clique decomposition theorems that characterize positive semidefinite and positive-semidefinite-completable matrices with chordal sparsity patterns. The paper describes a decomposition method that exploits partial separability in conic linear optimization. The method is based on Spingarn's method for equality constrained convex optimization, combined with a fast interior-point method for evaluating proximal operators

Sparse Bayesian Inference with Regularized Gaussian Distributions

Regularization is a common tool in variational inverse problems to impose assumptions on the parameters of the problem. One such assumption is sparsity, which is commonly promoted using lasso and total variation-like regularization. Although the solutions to many such regularized inverse problems can be considered as points of maximum probability of well-chosen posterior distributions, samples from these distributions are generally not sparse. In this paper, we present a framework for implicitly defining a probability distribution that combines the effects of sparsity imposing regularization with Gaussian distributions. Unlike continuous distributions, these implicit distributions can assign positive probability to sparse vectors. We study these regularized distributions for various regularization functions including total variation regularization and piecewise linear convex functions. We apply the developed theory to uncertainty quantification for Bayesian linear inverse problems and derive a Gibbs sampler for a Bayesian hierarchical model. To illustrate the difference between our sparsity-inducing framework and continuous distributions, we apply our framework to small-scale deblurring and computed tomography examples

The Splicing Efficiency of Activating HRAS Mutations Can Determine Costello Syndrome Phenotype and Frequency in Cancer

Costello syndrome (CS) may be caused by activating mutations in codon 12/13 of the HRAS proto-oncogene. HRAS p.Gly12Val mutations have the highest transforming activity, are very frequent in cancers, but very rare in CS, where they are reported to cause a severe, early lethal, phenotype. We identified an unusual, new germline p.Gly12Val mutation, c.35_36GC>TG, in a 12-year-old boy with attenuated CS. Analysis of his HRAS cDNA showed high levels of exon 2 skipping. Using wild type and mutant HRAS minigenes, we confirmed that c.35_36GC>TG results in exon 2 skipping by simultaneously disrupting the function of a critical Exonic Splicing Enhancer (ESE) and creation of an Exonic Splicing Silencer (ESS). We show that this vulnerability of HRAS exon 2 is caused by a weak 3' splice site, which makes exon 2 inclusion dependent on binding of splicing stimulatory proteins, like SRSF2, to the critical ESE. Because the majority of cancer- and CS- causing mutations are located here, they affect splicing differently. Therefore, our results also demonstrate that the phenotype in CS and somatic cancers is not only determined by the different transforming potentials of mutant HRAS proteins, but also by the efficiency of exon 2 inclusion resulting from the different HRAS mutations. Finally, we show that a splice switching oligonucleotide (SSO) that blocks access to the critical ESE causes exon 2 skipping and halts proliferation of cancer cells. This unravels a potential for development of new anti-cancer therapies based on SSO-mediated HRAS exon 2 skipping