Undersampling | EPFL Graph Search

In signal processing, undersampling or bandpass sampling is a technique where one samples a bandpass-filtered signal at a sample rate below its Nyquist rate (twice the upper cutoff frequency), but is still able to reconstruct the signal. When one undersamples a bandpass signal, the samples are indistinguishable from the samples of a low-frequency alias of the high-frequency signal. Such sampling is also known as bandpass sampling, harmonic sampling, IF sampling, and direct IF-to-digital conversion. Description The Fourier transforms of real-valued functions are symmetrical around the 0 Hz axis. After sampling, only a periodic summation of the Fourier transform (called discrete-time Fourier transform) is still available. The individual frequency-shifted copies of the original transform are called aliases. The frequency offset between adjacent aliases is the sampling-rate, denoted by fs. When the aliases are mutually exclusive (spectrally), the original transform an

Compressed sensing with signal averaging for improved sensitivity and motion artifact reduction in fluorine-19 MRI

Tom Hilbert, Tobias Kober, Elena Najdenovska, Ruud van Heeswijk, Jérôme Yerly

Fluorine-19 (F-19) MRI of injected perfluorocarbon emulsions (PFCs) allows for the non-invasive quantification of inflammation and cell tracking, but suffers from a low signal-to-noise ratio and extended scan time. To address this limitation, we tested the hypotheses that a(19)F MRI pulse sequence that combines a specific undersampling regime with signal averaging has both increased sensitivity and robustness against motion artifacts compared with a non-averaged fully sampled pulse sequence, when both datasets are reconstructed with compressed sensing. As a proof of principle, numerical simulations and phantom experiments were performed on selected variable ranges to characterize the point spread function of undersampling patterns, as well as the vulnerability to noise of undersampling and reconstruction parameters with paired numbers ofxsignal averages and acceleration factorx(NAx-AFx). The numerical simulations demonstrated that a probability density function that uses 25% of the samples to fully sample thek-space central area allowed for an optimal balance between limited blurring and artifact incoherence. At all investigated noise levels, the Dice similarity coefficient (DSC) strongly depended on the regularization parameters and acceleration factor. In phantoms, the motion robustness of an NA8-AF8 undersampling pattern versus NA1-AF1 was evaluated with simulated and real motion patterns. Differences were assessed with the DSC, which was consistently higher for the NA8-AF8 compared with the NA1-AF1 strategy, for both simulated and real cyclic motion patterns (P< 0.001). Both strategies were validated in vivo in mice (n= 2) injected with perfluoropolyether. Here, the images displayed a sharper delineation of the liver with the NA8-AF8 strategy than with the NA1-AF1 strategy. In conclusion, we validated the hypotheses that in(19)F MRI the combination of undersampling and averaging improves both the sensitivity and the robustness against motion artifacts.

WILEY2020

Fast model-based T-2 mapping using SAR-reduced simultaneous multislice excitation

Tom Hilbert, Tobias Kober, José Pedro Rebelo Ferreira Marques, Jean-Philippe Thiran

Purpose To obtain whole-brain high-resolution T-2 maps in 2 minutes by combining simultaneous multislice excitation and low-power PINS (power independent of number of slices) refocusing pulses with undersampling and a model-based reconstruction. Methods A multi-echo spin-echo sequence was modified to acquire multiple slices simultaneously, ensuring low specific absorption rate requirements. In addition, the acquisition was undersampled to achieve further acceleration. Data were reconstructed by subsequently applying parallel imaging to separate signals from different slices, and a model-based reconstruction to estimate quantitative T-2 from the undersampled data. The signal model used is based on extended phase graph simulations that also account for nonideal slice profiles and B-1 inhomogeneity. In vivo experiments with 3 healthy subjects were performed to compare accelerated T-2 maps to fully sampled single-slice acquisitions. The accuracy of the T-2 values was assessed with phantom experiments by comparing the T-2 values to single-echo spin-echo measurements. Results In vivo results showed that conventional multi-echo spin-echo, simultaneous multislice, and undersampling result in similar mean T-2 values within regions of interest. However, combining simultaneous multislice and undersampling results in higher SDs (about 7 ms) in comparison to a conventional sequence (about 3 ms). The T-2 values were reproducible between scan and rescan (SD < 1.2 ms) within subjects and were in similar ranges across subjects (SD < 4.5 ms). Conclusion The proposed method is a fast T-2 mapping technique that enables whole-brain acquisitions at 0.7-mm in-plane resolution, 3-mm slice thickness, and low specific absorption rate in 2 minutes.

WILEY2019

First results of correlation electron cyclotron emission on Tore Supra

Measurements of electron temperature fluctuations by means of correlation electron cyclotron emission (ECE) diagnostics aid in understanding the nature of the turbulent transport infusion plasmas. On Tore Supra tokamak, a 32-channel heterodyne ECE radiometer has been upgraded to include two channels for temperature fluctuation measurements. The central frequency of the yttrium iron garnet filter on each channel is remotely monitored by a driver, allowing one to shift the observation volume in the plasma radially. To resolve the fluctuation amplitude of 0.1%, integration times of similar to 3 s at 1 MHz sampling rate are required for the statistical error level of 0.05%. Together with the 32-channel profile radiometer, correlation ECE is a powerful and unique tool for simultaneous observation of the magnetohydrodynamic phenomena and studies of the plasma transport properties in various heating regimes during long-shot multimegawatt operation. First measurements of temperature fluctuations, of various origins, on Tore Supra (including the observation of the toroidicity-induced Alfven eigenmodes), as well as a description of the analysis methods used in the data evaluation, are reported in this paper.

2006

Compressed sensing with signal averaging for improved sensitivity and motion artifact reduction in fluorine-19 MRI

Tom Hilbert, Tobias Kober, Elena Najdenovska, Ruud van Heeswijk, Jérôme Yerly

WILEY2020