Half-quadratic regularization for MRI image restoration

We consider the reconstruction of MRI images by minimizing regularized cost-functions. To accelerate the computation of the estimate, two forms of half-quadratic regularization, multiplicative and additive, are often used. In Nikolova and Ng (2002), we have compared both theoretically and experimentally the efficiency of these two forms using one-dimensional signals. The goal of this paper is to compare experimentally the efficiency of these two forms using MRI image reconstruction. We find that using the additive form is more computationally effective than using the multiplicative form.published_or_final_versio

Efficient and Consistent Recursive Filtering of Images with Reflective Extension

Recursive filters are commonly used in scale space construction for their efficiency and simple implementation. However these filters have an initialisation problem which either produces unusable results near the image boundaries or requires costly approximate solutions such as extending the boundary manually. In this paper, we describe a method for the recursive filtering of reflectively extended images for filters with symmetric denominator. We begin with an analysis of reflective extensions and their effect on non-recursive filtering operators. Based on the non-recursive case, we derive a formulation of recursive filtering on reflective domains as a linear but time-varying implicit operator. We then give an efficient method for decomposing and solving the linear implicit system. This decomposition needs to be performed only once for each dimension of the image. This yields a filtering which is both stable and consistent with the ideal infinite extension. The filter is efficient, requiring the same order of computation as the standard recursive filtering. We give experimental evidence to verify these claims

Detection of Multiple Pathways in the Spinal Cord White Matter Using Q-Ball Imaging

International audienceHigh angular resolution MRI such as q-ball imaging (QBI) allows to recover complex white matter architecture. We applied this technique to an ex vivo spinal cord of one cat using a 3T scanner, 100 directions and b-values varying from 1000 to 3000 s/mm2. As a result, QBI can retrieve crossing fibre information, where the diffusion tensor imaging approach is constrained to a single diffusion direction. To our knowledge, this is the first study demonstrating the benefits of QBI in observing longitudinal, commissural and dorso-ventral fibres in the spinal cord. It is a first step towards in vivo characterization of the healthy and injured spinal cord using high angular resolution diffusion imaging (HARDI) and QBI

Indoor Calibration using Segment Chains

International audienceIn this paper, we present a new method for line segments matching for indoor reconstruction. Instead of matching individual seg- ments via a descriptor like most methods do, we match segment chains that have a distinctive topology using a dynamic programing formulation. Our method relies solely on the geometric layout of the segment chain and not on photometric or color profiles. Our tests showed that the presented method is robust and manages to produce calibration information even under a drastic change of viewpoint

Interpolating orientation fields : an axiomatic approach

International audienc

Unsupervised White Matter Fiber Clustering and Tract Probability Map Generation: Applications of a Gaussian Process framework for White Matter Fibers

With the increasing importance of fiber tracking in diffusion tensor images for clinical needs, there has been a growing demand for an objective mathematical framework to perform quantitative analysis of white matter fiber bundles incorporating their underlying physical significance. This paper presents such a novel mathematical framework that facilitates mathematical operations between tracts using an inner product based on Gaussian processes, between fibers which span a metric space. This metric facilitates combination of fiber tracts, rendering operations like tract membership to a bundle or bundle similarity simple. Based on this framework, we have designed an automated unsupervised atlas-based clustering method that does not require manual initialization nor an a priori knowledge of the number of clusters. Quantitative analysis can now be performed on the clustered tract volumes across subjects thereby avoiding the need for point parametrization of these fibers, or the use of medial or envelope representations as in previous work. Experiments on synthetic data demonstrate the mathematical operations. Subsequently, the applicability of the unsupervised clustering framework has been demonstrated on a 21 subject dataset