Piero Barone

A new method of magnetic resonance image reconstruction with short acquisition time and truncation artifact reduction

A method for the reconstruction of magnetic resonance images that allows for a substantial reduction of the quantity of measured data and, therefore, of the acquisition time is described. The truncation artifact is also reduced, improving the image quality. The method is based on techniques for getting superresolution in spectral analysis such as autoregressive modeling and Pronys method. Moreover, some new ideas about the autoregressive order selection are introduced. The method is compared to the standard one for reconstructing simulated, phantom, and medical magnetic resonance images. The numerical stability and the computational cost issues of the resulting algorithm are also addressed.

Mathematical principles of basic magnetic resonance imaging in medicine

Abstract In this paper we review, from a mathematical point of view, the main techniques of magnetic resonance imaging (MRI) used in medicine. A detailed mathematical description of the basic physics and of the image formation process is given in the framework of the classical theory.

Truncation artifact reduction in magnetic resonance imaging by Markov random field methods

A new statistical method is proposed for reduction of truncation artifacts when reconstructing a function by a finite number of its Fourier series coefficients. Following the Bayesian approach, it is possible to take into account both the errors induced by the truncation of the Fourier series and some specific characteristics of the function. A suitable Markov random field is used for modeling these characteristics. Furthermore, in applications like Magnetic Resonance Imaging, where these coefficients are the measured data, the experimental random noise in the data can also be taken into account. Monte Carlo Markov chain methods are used to make statistical inference. Parameter selection in the Bayesian model is also addressed and a solution for selecting the parameters automatically is proposed. The method is applied successfully to both simulated and real magnetic resonance images.

Bayesian estimation of relaxation times T1 in MR images of irradiated Fricke-agarose gels

The authors present a novel method for processing T(1)-weighted images acquired with Inversion-Recovery (IR) sequence. The method, developed within the Bayesian framework, takes into account a priori knowledge about the spatial regularity of the parameters to be estimated. Inference is drawn by means of Markov Chains Monte Carlo algorithms. The method has been applied to the processing of IR images from irradiated Fricke-agarose gels, proposed in the past as relative dosimeter to verify radiotherapeutic treatment planning systems. Comparison with results obtained from a standard approach shows that signal-to noise ratio (SNR) is strongly enhanced when the estimation of the longitudinal relaxation rate (R1) is performed with the newly proposed statistical approach. Furthermore, the method allows the use of more complex models of the signal. Finally, an appreciable reduction of total acquisition time can be obtained due to the possibility of using a reduced number of images. The method can also be applied to T(1) mapping of other systems.

Over-relaxation methods and coupled Markov chains for Monte Carlo simulation

This paper is concerned with improving the performance of certain Markov chain algorithms for Monte Carlo simulation. We propose a new algorithm for simulating from multivariate Gaussian densities. This algorithm combines ideas from coupled Markov chain methods and from an existing algorithm based only on over-relaxation. The rate of convergence of the proposed and existing algorithms can be measured in terms of the square of the spectral radius of certain matrices. We present examples in which the proposed algorithm converges faster than the existing algorithm and the Gibbs sampler. We also derive an expression for the asymptotic variance of any linear combination of the variables simulated by the proposed algorithm. We outline how the proposed algorithm can be extended to non-Gaussian densities.

General over-relaxation Markov chain Monte Carlo algorithms for Gaussian densities ☆

We study general over-relaxation Markov chain Monte Carlo samplers for multivariate Gaussian densities. We provide conditions for convergence based on the spectral radius of the transition matrix and on detailed balance. We illustrate these algorithms using an image analysis example.

Quantifying Human Brain Connectivity from Diffusion Tensor MRI

A new approach for quantifying the degree of connectivity between human brain regions from Diffusion Tensor Magnetic Resonance Imaging (DT-MRI) data is presented. To this aim, a functional is proposed and its theoretical properties are shown. The connectivity between pairs of white matter points is quantified by minimizing the weighted length of the curves within white matter connecting the points to each other. The weighting factor is a decreasing function of the diffusion coefficient along the curve tangent. This coefficient is a linear function of the diffusion tensor components, which are estimated from DT-MRI data. As a by-product of the analysis, the minimizing curves connecting the two points are provided. The solution of the minimization problem is obtained numerically by approximating the functional on a lattice and then solving a shortest path problem on an undirected weighted graph. The presented method is global and therefore not affected by problems due to fiber branching and crossing. It is also automatic and fast. Some results obtained from the implementation of this method on real data in physiological and simulated pathological conditions are illustrated.

Solving an Inverse Diffusion Problem for Magnetic Resonance Dosimetry by a Fast Regularization Method

An inverse diffusion problem that appears in Magnetic Resonance dosimetry is studied. The problem is shown to be equivalent to a deconvolution problem with a known kernel. To cope with the singularity of the kernel, nonlinear regularization functionals are considered which can provide regular solutions, reproduce steep gradients and impose positivity constraints. A fast deterministic algorithm for solving the involved non-convex minimization problem is used. Accurate restorations on real 256×256 images are obtained by the algorithm in a few minutes on a 266-MHz PC that allow to precisely quantitate the relative absorbed dose.