Multichannel Sampling of Pulse Streams at the Rate of Innovation

We consider minimal-rate sampling schemes for infinite streams of delayed and weighted versions of a known pulse shape. The minimal sampling rate for these parametric signals is referred to as the rate of innovation and is equal to the number of degrees of freedom per unit time. Although sampling of infinite pulse streams was treated in previous works, either the rate of innovation was not achieved, or the pulse shape was limited to Diracs. In this paper we propose a multichannel architecture for sampling pulse streams with arbitrary shape, operating at the rate of innovation. Our approach is based on modulating the input signal with a set of properly chosen waveforms, followed by a bank of integrators. This architecture is motivated by recent work on sub-Nyquist sampling of multiband signals. We show that the pulse stream can be recovered from the proposed minimal-rate samples using standard tools taken from spectral estimation in a stable way even at high rates of innovation. In addition, we address practical implementation issues, such as reduction of hardware complexity and immunity to failure in the sampling channels. The resulting scheme is flexible and exhibits better noise robustness than previous approaches

Innovation Rate Sampling of Pulse Streams with Application to Ultrasound Imaging

Signals comprised of a stream of short pulses appear in many applications including bio-imaging and radar. The recent finite rate of innovation framework, has paved the way to low rate sampling of such pulses by noticing that only a small number of parameters per unit time are needed to fully describe these signals. Unfortunately, for high rates of innovation, existing sampling schemes are numerically unstable. In this paper we propose a general sampling approach which leads to stable recovery even in the presence of many pulses. We begin by deriving a condition on the sampling kernel which allows perfect reconstruction of periodic streams from the minimal number of samples. We then design a compactly supported class of filters, satisfying this condition. The periodic solution is extended to finite and infinite streams, and is shown to be numerically stable even for a large number of pulses. High noise robustness is also demonstrated when the delays are sufficiently separated. Finally, we process ultrasound imaging data using our techniques, and show that substantial rate reduction with respect to traditional ultrasound sampling schemes can be achieved.Comment: 14 pages, 13 figure

Spectroscopy of 13B via the 13C(t,3He) reaction at 115 AMeV

Gamow-Teller and dipole transitions to final states in 13B were studied via the 13C(t,3He) reaction at Et = 115 AMeV. Besides the strong Gamow-Teller transition to the 13B ground state, a weaker Gamow-Teller transition to a state at 3.6 MeV was found. This state was assigned a spin-parity of 3/2- by comparison with shell-model calculations using the WBP and WBT interactions which were modified to allow for mixing between nhw and (n+2)hw configurations. This assignment agrees with a recent result from a lifetime measurement of excited states in 13B. The shell-model calculations also explained the relatively large spectroscopic strength measured for a low-lying 1/2+ state at 4.83 MeV in 13B. The cross sections for dipole transitions up to Ex(13B)= 20 MeV excited via the 13C(t,3He) reaction were also compared with the shell-model calculations. The theoretical cross sections exceeded the data by a factor of about 1.8, which might indicate that the dipole excitations are "quenched". Uncertainties in the reaction calculations complicate that interpretation.Comment: 11 pages, 6 figure

Spatial variability and changes of metabolite concentrations in the cortico-spinal tract in multiple sclerosis using coronal CSI

We characterized metabolic changes along the cortico-spinal tract (CST) in multiple sclerosis (MS) patients using a novel application of chemical shift imaging (CSI) and considering the spatial variation of metabolite levels. Thirteen relapsing-remitting (RR) and 13 primary-progressive (PP) MS patients and 16 controls underwent (1)H-MR CSI, which was applied to coronal-oblique scans to sample the entire CST. The concentrations of the main metabolites, i.e., N-acetyl-aspartate, myo-Inositol (Ins), choline containing compounds (Cho) and creatine and phosphocreatine (Cr), were calculated within voxels placed in regions where the CST is located, from cerebral peduncle to corona radiata. Differences in metabolite concentrations between groups and associations between metabolite concentrations and disability were investigated, allowing for the spatial variability of metabolite concentrations in the statistical model. RRMS patients showed higher CST Cho concentration than controls, and higher CST Ins concentration than PPMS, suggesting greater inflammation and glial proliferation in the RR than in the PP course. In RRMS, a significant, albeit modest, association between greater Ins concentration and greater disability suggested that gliosis may be relevant to disability. In PPMS, lower CST Cho and Cr concentrations correlated with greater disability, suggesting that in the progressive stage of the disease, inflammation declines and energy metabolism reduces. Attention to the spatial variation of metabolite concentrations made it possible to detect in patients a greater increase in Cr concentration towards the superior voxels as compared to controls and a stronger association between Cho and disability, suggesting that this step improves our ability to identify clinically relevant metabolic changes

A high efficiency, low background detector for measuring pair-decay branches in nuclear decay

We describe a high efficiency detector for measuring electron-positron pair transitions in nuclei. The device was built to be insensitive to gamma rays and to accommodate high overall event rates. The design was optimized for total pair kinetic energies up to about 7 MeV.Comment: Accepted for publication by Nucl. Inst. & Meth. in Phys. Res. A (NIM A

The Influence of Quadrature Errors on Isogeometric Mortar Methods

Mortar methods have recently been shown to be well suited for isogeometric analysis. We review the recent mathematical analysis and then investigate the variational crime introduced by quadrature formulas for the coupling integrals. Motivated by finite element observations, we consider a quadrature rule purely based on the slave mesh as well as a method using quadrature rules based on the slave mesh and on the master mesh, resulting in a non-symmetric saddle point problem. While in the first case reduced convergence rates can be observed, in the second case the influence of the variational crime is less significant