Application of the chirp z-transform to MRI data

Reconstruction of partial envelope of interference pattern based on chirp Z-transform

This paper presents a novel algorithm for the partial reconstruction of interference pattern envelopes. In multi-pulse train interferometers, the exact determination of the peak position of the envelope of interference fringes is of paramount importance. The estimation of the interference pattern envelope usually involves the use of discrete Fourier transform (DFT). The proposed algorithm is based on the chirp Z-transform (CZT) instead of DFT and avoids estimating the entire envelope of the interference pattern. It is sufficient for determining part of the envelope around the peak value position. The proposed approach is presented and illustrated for the first time by means of optical fringes. The experimental results demonstrate that this approach is reliable for partial envelope determination.

Low-field permanent magnets for industrial process and quality control

In this review we focus on the technology associated with low-field NMR. We present the current state-of-the-art in low-field NMR hardware and experiments, considering general magnet designs, rf performance, data processing and interpretation. We provide guidance on obtaining the optimum results from these instruments, along with an introduction for those new to low-field NMR. The applications of lowfield NMR are now many and diverse. Furthermore, niche applications have spawned unique magnet designs to accommodate the extremes of operating environment or sample geometry. Trying to capture all the applications, methods, and hardware encompassed by low-field NMR would be a daunting task and likely of little interest to researchers or industrialists working in specific subject areas. Instead we discuss only a few applications to highlight uses of the hardware and experiments in an industrial environment. For details on more particular methods and applications, we provide citations to specialized review articles.

Single acquisition quantitative single-point electron paramagnetic resonance imaging

PURPOSE

Electron paramagnetic resonance imaging has emerged as a promising noninvasive technology to dynamically image tissue oxygenation. Owing to its extremely short spin-spin relaxation times, electron paramagnetic resonance imaging benefits from a single-point imaging scheme where the entire free induction decay signal is captured using pure phase encoding. However, direct T2 (*)/pO2 quantification is inhibited owing to constant magnitude gradients which result in time-decreasing field of view. Therefore, conventional acquisition techniques require repeated imaging experiments with differing gradient amplitudes (typically 3), which results in long acquisition time.

METHODS

In this study, gridding was evaluated as a method to reconstruct images with equal field of view to enable direct T2 (*)/pO2 quantification within a single imaging experiment. Additionally, an enhanced reconstruction technique that shares high spatial k-space regions throughout different phase-encoding time delays was investigated (k-space extrapolation).

RESULTS

The combined application of gridding and k-space extrapolation enables pixelwise quantification of T2 (*) from a single acquisition with improved image quality across a wide range of phase-encoding time delays. The calculated T2 (*)/pO2 does not vary across this time range.

CONCLUSIONS

By utilizing gridding and k-space extrapolation, accurate T2 (*)/pO2 quantification can be achieved within a single data set to allow enhanced temporal resolution (by a factor of 3).

Multi-Frame SPRITE: a method for resolution enhancement of multiple-point SPRITE data

The Single Point Ramped Imaging with T1 Enhancement (SPRITE) sequence is well suited for the acquisition of magnetic resonance signals from fast relaxing nuclei and from heterogeneous materials. However, it is time inefficient compared to sequences that are based on frequency encoding because only one single point is acquired per excitation. Multiple-point SPRITE (mSPRITE) mitigates this problem with the acquisition of multiple FID points. mSPRITE images reconstructed from early FID samples suffer from reduced spatial resolution due to the limited extent of its corresponding k-space. In this work we present a new reconstruction algorithm for spatial resolution enhancement that solves this problem without changes to the mSPRITE sequence. The method, called Multi-Frame mSPRITE, substitutes high spatial frequencies from late FID points into k-spaces of limited extent constructed from early FID points. In this way, images of high quality and resolution can be obtained despite a large range of zoom factors used to reconstruct images with the same FOV and resolution.

MR imaging of ore for heap bioleaching studies using pure phase encode acquisition methods

Various MRI techniques were considered with respect to imaging of aqueous flow fields in low grade copper ore. Spin echo frequency encoded techniques were shown to produce unacceptable image distortions which led to pure phase encoded techniques being considered. Single point imaging multiple point acquisition (SPI-MPA) and spin echo single point imaging (SESPI) techniques were applied. By direct comparison with X-ray tomographic images, both techniques were found to be able to produce distortion-free images of the ore packings at 2 T. The signal to noise ratios (SNRs) of the SESPI images were found to be superior to SPI-MPA for equal total acquisition times; this was explained based on NMR relaxation measurements. SESPI was also found to produce suitable images for a range of particles sizes, whereas SPI-MPA SNR deteriorated markedly as particles size was reduced. Comparisons on a 4.7 T magnet showed significant signal loss from the SPI-MPA images, the effect of which was accentuated in the case of unsaturated flowing systems. Hence it was concluded that SESPI was the most robust imaging method for the study of copper ore heap leaching hydrology.

Quantitative single point imaging with compressed sensing

A novel approach with respect to single point imaging (SPI), compressed sensing, is presented here that is shown to significantly reduce the loss of accuracy of reconstructed images from under-sampled acquisition data. SPI complements compressed sensing extremely well as it allows unconstrained selection of sampling trajectories. Dynamic processes featuring short T2* NMR signal can thus be more rapidly imaged, in our case the absorption of moisture by a cereal-based wafer material, with minimal loss of image quantification. The absolute moisture content distribution is recovered via a series of images acquired with variable phase encoding times allowing extrapolation to time zero for each image pixel and the effective removal of T2* contrast.

Phase-cycled averaging for the suppression of residual magnetisation in SPI sequences

Residual magnetisation is one of the major sources of artefacts in single point imaging sequences with short repetition times. The unwanted signal is caused by non-dephased transverse magnetisation excited in preceding acquisition cycles. Therefore, the problem emerges mainly around the centre of k-space and has been solved in the past by additional spoiling gradients. In this work, unwanted residual magnetisation acquired with the SPRITE sequence was investigated and a new method for the suppression of residual magnetisation is presented. It is shown that residual magnetisation experiences a different phase encoding leading to residual images with a different FOV. A phase cycling filter is able to eliminate the unwanted signal. Furthermore, a description of all signal components that occur is presented using an operator notation. The notation is new in this field with respect to its completeness. That is, the signal description is based on an understanding of single point imaging sequences, such as SPRITE, by the use of an extended phase encode graph. A prominent in vivo example is that of sodium imaging in biological tissue where transverse relaxation times are such that unwanted coherences can occur and therefore residual magnetisation becomes a significant problem. For instance, sodium in biological tissue has two transverse relaxation times of approximately 3ms and 15ms at 4T and this can result in significant artefacts if the encoding time is short and TR<<3ms.

Optimal k-space sampling for single point imaging of transient systems

A novel approach for sampling k-space in a pure phase encoding imaging sequence is presented using the Single Point Imaging (SPI) technique. The sequence is optimised with respect to the achievable Signal-to-Noise ratio (SNR) for a given time interval via selective sparse k-space sampling, dictated by prior knowledge of the overall object of interest's shape. This allows dynamic processes featuring short T(2)( *) NMR signal to be more readily followed, in our case the absorption of moisture by a cereal-based wafer material. Further improvements in image quality are also shown via the use of complete sampling of k-space at the start or end of the series of imaging experiments; followed by subsequent use of this data for un-sampled k-space points as opposed to zero filling.