We propose a stochastic algorithm for solving NP-hard combinatorial optimization problems and study its convergence

Dynamic magnetic resonance imaging with contrast agent is a very promising technique for mammography. A temporal sequence of magnetic resonance images of the same slice are acquired following the injection of a contrast agent in the blood stream. The image intensity depends on the local concentration of the contrast agent so that tissue perfusion can be studied using the image sequence. A new statistical method of analyzing such sequences is presented. The method is developed within the Bayesian framework. A specific statistical model is used to take into account image degradation. In addition, a suitable Markov random field allows us to model some relevant ``a priori'' information on the quantities to be estimated. Inference is based on simulations from the posterior distribution obtained by means of Markov chain algorithms. The issue of hyper-parameter estimation is also addressed. Image classification is also performed by means of a new Bayesian method. Some results obtained from sequences of dynamic magnetic resonance images of human breasts will be illustrated.

Col lavoro svolto nel periodo triennale del progetto si sono sviluppati nuovi metodi bayesiani per l'analisi di immagini dinamiche di risonanza magnetica (RM) per lo studio e la diagnosi di tumori della mammella. I metodi sono stati implementati realizzando il software ``Bandits'', che puo' essere utilizzato su PC/Windows senza altro software di calcolo scientifico. Il software e' stato usato ed apprezzato dai radiologi dell'unita' operativa dell'Istituto Regina Elena, coinvolti nella ricerca. Seppure i metodi siano stati specializzati alla RM per lo studio dei tumori della mammella, essi possono essere utilizzati, con modifiche di piccola o media entita', con immagini di diverso tipo (TAC) e/o per applicazioni diverse. Il software migliora la qualita' delle immagini riducendone le distorsioni causate dalle imperfezioni strumentali e dal movimento del paziente. Viene inoltre effettuata una sintesi dell'informazione contenuta nelle immagini della sequenza dinamica attraverso due sole immagini che rappresentano parametri di diretta interpretazione per il clinico. A partire da queste due immagini, e' poi possibile classificare i pixel dell'immagine in un numero di classi opportuno, che corrispondono ai diversi tessuti (es.: sano, tumorale benigno o maligno, necrotico)

The problem of classifying multispectral image data is studied here. We propose a new Bayesian method for this. The method uses "a priori" spatial information modeled by means of a suitable Markov random field. The image data for each class are assumed to be i.i.d. following a multivariate Gaussian model with unknown mean and unknown diagonal covariance matrix. When the prior information is not used and the variances of the Gaussian model are equal, the method reduces to the standard K-means algorithm. All the parameters appearing in the posterior model are estimated simultaneously. The prior normalizing constant is approximated on the basis of the expectation of the energy function as obtained by means of Markov Chain Monte Carlo simulations. Some experimental results suggest calculating this expectation from a "standard" function by simple multiplication by the minimum value of the energy. A local solution to the problem of maximizing the posterior distribution is obtained by using the Iterated Conditional Modes algorithm. The implementation of this method is easy and the required computations are carried out quickly, The method was applied with success to classify simulated image data and real dynamic Magnetic Resonance Imaging data.

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.

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.

In this paper we study several different methods both deterministic and stochastic to solve the Nuclear Magnetic Resonance (NMR) relaxometry problem. This problem is strongly related to finding a non-negative function given a finite number of values of its Laplace transform embedded in noise. Some of the methods considered here are new. We also propose a procedure which exploits and combines the main features of these methods. To show the performances of this procedure, some results of applying it to synthetic data are finally reported.

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.

Recent studies have demonstrated the potential of dynamic contrast-enhanced magnetic resonance imaging (MRI) describing pulmonary perfusion. However, breathing motion, susceptibility artifacts, and a low signal-to-noise ratio (SNR) make automatic pixel-by-pixel analysis difficult. In the present work, we propose a novel method to compensate for breathing motion. In order to test the feasibility of this method, we enrolled 53 patients with pulmonary embolism (N = 24), chronic obstructive pulmonary disease (COPD) (N = 14), and acute pneumonia (N = 15). A crucial part of the method, an automatic diaphragm detection algorithm, was evaluated in all 53 patients by two independent observers. The accuracy of the method to detect the diaphragm showed a success rate of 92%. Furthermore, a Bayesian noise reduction technique was implemented and tested. This technique significantly reduced the noise level without removing important clinical information. In conclusion, the combination of a motion correction method and a Bayesian noise reduction method offered a rapid, semiautomatic pixel-by-pixel analysis of the lungs with great potential for research and clinical use. © 2001 Wiley-Liss, Inc.

The authors present a novel method for processing T1-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 T1 mapping of other systems.