The filtering approach to solvent peak suppression in MRS: a critical review

Suppressing the solvent peak is important in many applications of biomedical NMR spectroscopy in order to quantify the metabolites with a great accuracy. Among the postprocessing methods proposed in the literature, many deal with the concept of filtering. However, several proposals lack a theoretical perspective and some have not been explicitly applied to quantification problems. The present article is intended to bridge this gap: five methods are analyzed from a theoretical perspective. Subsequently the different methods are applied to the same set of data, and then the latter are quantified using the model fitting method AMARES. With our set, the scheme proposed by T. Sundin et al. (J. Magn. Reson. 139(2), 189-204 (1999)) proved to be the most reliable method.     

Periodic solutions of a nonlinear wave equation without assumption of monotonicity

Mathematische Annalen -     

A variant of Boneh-Franklin IBE with a tight reduction in the random oracle model

The first practical identity based encryption (IBE) scheme was published by Boneh and Franklin at Crypto 2001, based on the elliptic curve pairing. Since that time, many other IBE schemes have been published. In this paper, we describe a variant of Boneh-Franklin with a tight reduction in the random oracle model. Our new scheme is quite efficient compared to existing schemes; moreover, upgrading from Boneh-Franklin to our new scheme is straightforward.      

Dual-mode registration of dynamic contrast-enhanced ultrasound combining tissue and contrast sequences

This study proposes a new method for automatic, iterative image registration in the context of dynamic contrast-enhanced ultrasound (DCE-US) imaging. By constructing a cost function of image registration using a combination of the tissue and contrast-microbubble responses, this new method, referred to as dual-mode registration, performs alignment based on both tissue and vascular structures. Data from five focal liver lesions (FLLs) were used for the evaluation. Automatic registration based on the dual-mode registration technique and tissue-mode registration obtained using the linear response image sequence alone were compared to manual alignment of the sequence by an expert. Comparison of the maximum distance between the transformations applied by the automatic registration techniques and those from expert manual registration reference showed that the dual-mode registration provided better precision than the tissue-mode registration for all cases. The reduction of maximum distance ranged from 0.25 to 9.3 mm. Dual-mode registration is also significantly better than tissue-mode registration for the five sequences with p  -values lower than 0.03$0.03$. The improved sequence alignment is also demonstrated visually by comparison of images from the sequences and the video playbacks of the motion-corrected sequences. This new registration technique better maintains a selected region of interest (ROI) within a fixed position of the image plane throughout the DCE-US sequence. This should reduce motion-related variability of the echo-power estimations and, thus, contribute to more robust perfusion quantification with DCE-US.     

On the small-time local controllability of a quantum particle in a moving one-dimensional infinite square potential well

We consider a quantum charged particle in a one-dimensional infinite square potential well moving along a line. We control the acceleration of the potential well. The local controllability in large time of this nonlinear control system along the ground state trajectory has been proved recently. We prove that this local controllability does not hold in small time, even if the Schrödinger equation has an infinite speed of propagation. To cite this article: J.-M. Coron, C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

Water peak suppression: time-frequency vs time-scale approach

Wavelets are the most popular time-scale analysis tool. A well-known application of wavelets in nuclear magnetic resonance spectroscopy is water peak extraction/suppression. However, spectroscopists are more familiar with frequency than scale. So, from a spectroscopist point of view, a time-scale analysis tool (i.e., wavelets) is not natural and a time-frequency approach would be much more satisfactory. We explain a time-frequency solution to this problem based on Gabor analysis. As the two formalisms are closely linked together we continuously emphasize their similarities and differences. In particular we show that, here, the Gabor method is as efficient as the wavelet approach, and we give some examples. Those remarks also apply to other NMR problems solved previously with the continuous wavelet transform, such as quantification or dynamical phase correction.     

Controllability Issues for Continuous-Spectrum Systems and Ensemble Controllability of Bloch Equations

We study the controllability of the Bloch equation, for an ensemble of non interacting half-spins, in a static magnetic field, with dispersion in the Larmor frequency. This system may be seen as a prototype for infinite dimensional bilinear systems with continuous spectrum, whose controllability is not well understood. We provide several mathematical answers, with discrimination between approximate and exact controllability, and between finite time or infinite time controllability: this system is not exactly controllable in finite time T with bounded controls in L ²(0, T), but it is approximately controllable in L ^∞ in finite time with unbounded controls in L^￥_loc([0,+￥)){L^{\infty}_{loc}([0,+\infty))}. Moreover, we propose explicit controls realizing the asymptotic exact controllability to a uniform state of spin + 1/2 or −1/2.