Colas Schretter

Information-Theoretic Feature Selection in Microarray Data Using Variable Complementarity

The paper presents an original filter approach for effective feature selection in microarray data characterized by a large number of input variables and a few samples. The approach is based on the use of a new information-theoretic selection, the double input symmetrical relevance (DISR), which relies on a measure of variable complementarity. This measure evaluates the additional information that a set of variables provides about the output with respect to the sum of each single variable contribution. We show that a variable selection approach based on DISR can be formulated as a quadratic optimization problem: the dispersion sum problem (DSP). To solve this problem, we use a strategy based on backward elimination and sequential replacement (BESR). The combination of BESR and the DISR criterion is compared in theoretical and experimental terms to recently proposed information-theoretic criteria. Experimental results on a synthetic dataset as well as on a set of eleven microarray classification tasks show that the proposed technique is competitive with existing filter selection methods.

OligoFaktory: a visual tool for interactive oligonucleotide design

SUMMARY The OligoFaktory is a set of tools for the design, on an arbitrary number of target sequences, of high-quality long oligonucleotide for micro-array, of primer pair for PCR, of siRNA and more. The user-centered interface exists in two flavours: a web portal and a standalone software for Mac OS X Tiger. A unified presentation of results provides overviews with distribution charts and relative location bar graphs, as well as detailed features for each oligonucleotide. Input and output files conform to a common XML interchange file format to allow both automatic generation of input data, archiving, and post-processing of results. The design pipeline can use BLAST servers to evaluate specificity of selected oligonucleotides. AVAILABILITY The web portal http://ueg.ulb.ac.be/oligofaktory/; the software for Macintosh: http://www.oligofaktory.org/

A fast tube of response ray‐tracer

A ray-tracing algorithm is proposed to quickly approximate volumes of intersection between an arbitrary tube of response and a voxel array. The method is based on the idea of the Wu antialiased line tracer that is well known in the computer graphics community. However, our method works in three dimensions and supports arbitrary symmetrical response profile functions. The inner loop implementation does not use any conditional branching and is aware of low-level optimization strategies. The running speed of a fast incremental Siddon routine appears to be about 60% slower than our algorithm.

A direct inversion method for non-uniform quasi-random point sequences

Abstract. The inversion method is an effective approach for transforming uniform random points according to a given probability density function. In two dimensions, horizontal and vertical displacements are computed successively using a marginal and then all conditional density functions. When quasi-random low-discrepancy points are provided as input, spurious artifacts might appear if the density function is not separable. Therefore, this paper relies on combining intrinsic properties of the golden ratio sequence and the Hilbert space filling curve for generating non-uniform point sequences using a single step inversion method. Experiments show that this approach improves efficiency while avoiding artifacts for general discrete probability density functions.

Event-by-Event Image Reconstruction From List-Mode PET Data

This paper adapts the classical list-mode OSEM and the globally convergent list-mode COSEM methods to the special case of singleton subsets. The image estimate is incrementally updated for each coincidence event measured by the PET scanner. Events are used as soon as possible to improve the current image estimate, and, therefore, the convergence speed toward the maximum-likelihood solution is accelerated. An alternative online formulation of the list-mode COSEM algorithm is proposed first. This method saves memory resources by re-computing previous incremental image contributions while processing a new pass over the complete dataset. This online expectation-maximization principle is applied to the list-mode OSEM method, as well. Image reconstructions have been performed from a simulated dataset for the NCAT torso phantom and from a clinical dataset. Results of the classical and event-by-event list-mode algorithms are discussed in a systematic and quantitative way.

Golden Ratio Sequences for Low-Discrepancy Sampling

Abstract Most classical constructions of low-discrepancy point sets are based on generalizations of the one-dimensional binary van der Corput sequence, whose implementation requires nontrivial bit-operations. As an alternative, we introduce the quasi-regular golden ratio sequences, which are based on the fractional part of successive integer multiples of the golden ratio. By leveraging results from number theory, we show that point sets, which evenly cover the unit square or disc, can be computed by a simple incremental permutation of a generator golden ratio sequence. We compare ambient occlusion images generated with a Monte Carlo ray tracer based on random, Hammersley, blue noise, and golden ratio point sets. The source code of the ray tracer used for our experiments is available online at the address provided at the end of this article.

Image-based iterative compensation of motion artifacts in computed tomography

PURPOSE This article presents an iterative method for compensation of motion artifacts for slowly rotating computed tomography (CT) systems. Patients motion introduces inconsistencies among projections and yields severe reconstruction artifacts for free-breathing acquisitions. Streaks and doubling of structures can appear and the resolution is limited by strong blurring. METHODS The rationale of the proposed motion compensation method is to iteratively correct the reconstructed image by first decomposing the perceived motion in projection space, then reconstructing the motion artifacts in image space, and finally subtracting the artifacts from an initial image. The initial image is reconstructed from the acquired data and might contain motion blur artifacts but, nevertheless, is considered as a reference for estimating the reconstruction artifacts. RESULTS Qualitative and quantitative figures are shown for experiments based on numerically simulated projections of a sequence of clinical images resulting from a respiratory-gated helical CT acquisition. The border of the diaphragm becomes progressively sharper and the contrast improves for small structures in the lungs. CONCLUSIONS The originality of the technique stems from the fact that the patient motion is not explicitly estimated but the motion artifacts are reconstructed in image space. This approach could provide sharp static anatomical images on interventional C-arm systems or on slowly rotating X-ray equipments in radiotherapy.

Correction of some time-dependent deformations in parallel-beam computed tomography

In computed tomography on interventional X-ray systems, image quality is frequently degraded by uncontrolled patient motion such as breath-hold failures, intestinal contractions, or nervous shaking. To overcome this problem, an iterative workflow is proposed to estimate a dynamic displacement field representing the time-varying position of image elements. An elastic signal registration algorithm computes the displacement in projection space from the difference between measured projections and reference projections, sampled from the image reconstructed in previous iterations. Considering the sampled image as a motionless reference, the motion estimation is exact for a certain class of deformations, including shifting, expansion, and compression. From a new estimate of the displacement field, a better image can be reconstructed by introducing motion compensation in the backprojection step of filtered-backprojection methods. The result of the first iteration is equivalent to a standard reconstruction without motion correction and further iterations progressively sharpen the image.

Van der Corput and Golden Ratio Sequences Along the Hilbert Space-Filling Curve

This work investigates the star discrepancies and squared integration errors of two quasi-random points constructions using a generator one-dimensional sequence and the Hilbert space-filling curve. This recursive fractal is proven to maximize locality and passes uniquely through all points of the d-dimensional space. The van der Corput and the golden ratio generator sequences are compared for randomized integro-approximations of both Lipschitz continuous and piecewise constant functions. We found that the star discrepancy of the construction using the van der Corput sequence reaches the theoretical optimal rate when the number of samples is a power of two while using the golden ratio sequence performs optimally for Fibonacci numbers. Since the Fibonacci sequence increases at a slower rate than the exponential in base 2, the golden ratio sequence is preferable when the budget of samples is not known beforehand. Numerical experiments confirm this observation.

Sufficient condition for local invertibility of spatio-temporal 4D B-spline deformations

Recent advances in medical imaging technologies have made 4D image sequences available in clinical routine. As a consequence, image registration techniques are evolving from alignment of pairs of static volumetric images to spatio-temporal registration of dynamic (4D) images. Since the elastic image registration problem is ill-posed, additional prior information or constraints are usually required to regularize the problem. This work proposes to enforce local invertibility (diffeomorphism) of 4D deformations. A novel sufficient condition for local invertibility over continuous space and time is proposed and a practical regularization prior is designed from the theory. The method has been applied to an image registration (motion tracking) of a dynamic 4D CT image sequence. Results show that using proposed regularizer leads to deformations that are more plausible for respiratory motion than the standard approach without additional temporal regularization.