Rotation of NMR images using the 2D chirp-z transform

Correction algorithm of the frequency-modulated continuous-wave LIDAR ranging system

Frequency-modulated continuous-wave LIDAR has broad application prospects. Compared with the traditional pulse LIDAR, the FMCW LIDAR has the advantages of high resolution and long measurement distance. But it still can be affected by several factors, including environmental noise, spectrum aliasing, spectrum leakage and other issues. Some traditional filtering algorithms or signal transformation algorithms can improve the above problems, but the effect is not ideal. This paper proposes a signal correction algorithm called the VMD-based refined cross-power spectral density algorithm (VRCPSD). This algorithm is based on signal decomposition denoising and improved spectrum refinement methods. The algorithm applies variational mode decomposition, spectrum refinement and cross-power spectral density to signal processing. The VRCPSD algorithm is compared with the traditional spectrum correction algorithm on the high-speed linear array APD FMCW LIDAR experimental platform. The results show that the VRCPSD algorithm has a better spectrum correction effect on the LIDAR experimental platform. This algorithm can reduce the margin of error to the centimeter level. Therefore, the algorithm is promising in that it can improve the signal waveform of the FMCW laser radar ranging system, make the spectrum get better correction and make the distance more accurate.

Theory and algorithm of the homeomorphic Fourier transform for optical simulations

The introduction of the fast Fourier transform (FFT) constituted a crucial step towards a faster and more efficient physio-optics modeling and design, since it is a faster version of the Discrete Fourier transform. However, the numerical effort of the operation explodes in the case of field components presenting strong wavefront phases-very typical occurrences in optics- due to the requirement of the FFT that the wrapped phase be well sampled. In this paper, we propose an approximated algorithm to compute the Fourier transform in such a situation. We show that the Fourier transform of fields with strong wavefront phases exhibits a behavior that can be described as a bijective mapping of the amplitude distribution, which is why we name this operation "homeomorphic Fourier transform." We use precisely this characteristic behavior in the mathematical approximation that simplifies the Fourier integral. We present the full theoretical derivation and several numerical applications to demonstrate its advantages in the computing process.

Practically Lossless Affine Image Transformation

In this contribution we introduce an almost lossless affine 2D image transformation method. To this end we extend the theory of the well-known Chirp-z transform to allow for fully affine transformation of general n-dimensional images. In addition we give a practical spatial and spectral zero-padding approach dramatically reducing losses of our transform, where usual transforms introduce blurring artifacts due to sub-optimal interpolation. The proposed method improves the mean squared error by approx. a factor of 1800 compared to the commonly used linear interpolation, and by a factor of 250 to the best competitor. We derive the transform from basic principles with special attention to implementation details and supplement this paper with python code for 2D images. In demonstration experiments we show the superior image quality compared to usual approaches, when using our method. However runtimes are considerably larger than when using toolbox algorithms.

Application of the semi-analytical Fourier transform to electromagnetic modeling

The Fast Fourier Transform (FFT) algorithm makes up the backbone of fast physical optics modeling. Its numerical effort, approximately linear on the sample number of the function to be transformed, already constitutes a huge improvement on the original Discrete Fourier Transform. However, even this orders-of-magnitude improvement in the number of operations required can fall short in optics, where the tendency is to work with field components that present strong wavefront phases: this translates, as per the Nyquist-Shannon sampling theorem, into a huge sample number. So much so, in fact, that even with the reduced effort of the FFT, the operation becomes impracticable. Finding a workaround that allows us to evade, at least in part, these stringent sampling requirements is then fundamental for the practical feasibility of the Fourier transform in optics. In this work we propose, precisely, a way to tackle the Fourier transform that eschews the sampling of second-order polynomial phase terms, handling them analytically instead: it is for this reason that we refer to this method as the "semi-analytical Fourier transform". We present here the theory behind this concept and show the algorithm in action at several examples which serve to illustrate the vast potential of this approach.

Phase retrieval with unknown sampling factors via the two-dimensional chirp z-transform

We derive the analytic gradient of a phase retrieval error metric with respect to the sampling factor or the f-number that produced the measured point-spread function. This allows us to efficiently optimize over the sampling factor, thereby improving the accuracy of the phase estimate. Computer simulation results show its effectiveness.

Volumetric navigators for real-time motion correction in diffusion tensor imaging

Prospective motion correction methods using an optical system, diffusion-weighted prospective acquisition correction, or a free induction decay navigator have recently been applied to correct for motion in diffusion tensor imaging. These methods have some limitations and drawbacks. This article describes a novel technique using a three-dimensional-echo planar imaging navigator, of which the contrast is independent of the b-value, to perform prospective motion correction in diffusion weighted images, without having to reacquire volumes during which motion occurred, unless motion exceeded some preset thresholds. Water phantom and human brain data were acquired using the standard and navigated diffusion sequences, and the mean and whole brain histogram of the fractional anisotropy and mean diffusivity were analyzed. Our results show that adding the navigator does not influence the diffusion sequence. With head motion, the whole brain histogram-fractional anisotropy shows a shift toward lower anisotropy with a significant decrease in both the mean fractional anisotropy and the fractional anisotropy histogram peak location (P<0.01), whereas the whole brain histogram-mean diffusivity shows a shift toward higher diffusivity with a significant increase in the mean diffusivity (P<0.01), even after retrospective motion correction. These changes in the mean and the shape of the histograms are recovered substantially in the prospective motion corrected data acquired using the navigated sequence.

Preserving the accuracy and resolution of the sodium bioscale from quantitative sodium MRI during intrasubject alignment across longitudinal studies

Emerging applications of sodium bioscales derived from quantitative sodium magnetic resonance imaging assess temporal changes in regional sodium concentration over intervals that vary from hours (monitoring tissue viability in stroke) to weeks (monitoring brain tumor treatment during radiation therapy) or even years (monitoring progression of neurodegenerative disease). Accurate interpretation of such quantitative data requires precise registration between magnetic resonance imaging sessions to avoid session-to-session changes in partial volume effects between normal tissue (∼38 mM sodium concentration), lesions (variable sodium concentration), and cerebrospinal fluid (∼144 mM sodium concentration). The existing Automated Image Registration algorithm is shown to be suitable for rapid, accurate, and precise determination of the transform that aligns sodium magnetic resonance images. Implementation of this transform during image reconstruction from the k-space data is shown to produce smaller errors than conventional image-domain interpolation. Experimental results at 9.4 T and 3.0 T demonstrating this registration approach to sodium data illustrate preservation of quantification accuracy during alignment of sodium magnetic resonance images acquired from the same subject during different imaging sessions.

An evaluation of prefiltered reconstruction schemes for volume rendering

In this paper prefiltered reconstruction techniques are evaluated for volume-rendering applications. All the analyzed methods perform a discrete prefiltering as a preprocessing of the input samples in order to improve the quality of the continuous reconstruction afterwards. Various prefiltering schemes have been proposed to fulfill either spatial-domain or frequency domain criteria. According to our best knowledge, however, their thorough comparative study has not been published yet. Therefore we derive the frequency responses of the different prefilteredreconstruction techniques to analyze their global behavior such as aliasing or smoothing. Furthermore, we introduce a novel mathematical basis to compare also their spatial-domain behavior in terms of the asymptotic local error effect. For the sake of fair comparison, we use the same linear and cubic B-splines as basis functions but combined with different discrete prefilters. Our goal with this analysis is to help the potential users to select the optimal prefiltering scheme for their specific applications.

Application of the chirp z-transform to MRI data

A version of the chirp z-transform (CZT) enabling signal intensity and phase-preserving field-of-view scaling has been programmed. The algorithm is important for all single-point imaging sequences such as SPRITE when used with multiple data acquisition for T2* mapping or signal averaging. CZT has particular utility for SPRITE imaging of nuclei with short relaxation times such as sodium at high field. Here, a complete theory of the properties of CZT is given. This method operates entirely in k-space. It is compared with a conventional interpolation approach that works in image space after the application of a fast Fourier transformation.

Head motion suppression using real-time feedback of motion information and its effects on task performance in fMRI

A voluntary head motion suppression method using feedback to subjects of their own head motion information is demonstrated. A real-time fMRI system was developed on standard MR imaging hardware for this purpose. The head motion information was simplified as a four-way arrow display that changed color from green to red when a composite head motion index went beyond a specified threshold. The arrow indicators were integrated into a version of the commonly used visual N-BACK task. Results suggest a significant suppression of head motion consistently in all subjects while the influence on task performance and brain activation was minimal. It is proposed that under certain experimental conditions, voluntary head motion suppression may feasibly be employed without significant compromise of fMRI data.

RINGLET motion correction for 3D MRI acquired with the elliptical centric view order

A new rigid-body motion correction algorithm is described that is compatible with 3D image sets acquired with the elliptical centric (EC) view order. With this view order, an annular ring of k-space data is acquired in the ky-kz plane during any short time interval. Images for tracking motion can be reconstructed in the yz-plane from any ring of the acquisition data. In these tracking images, a point source (such as an external marker) shows a characteristic bull's-eye pattern that permits motion monitoring and correction. The true position of the point object is located at the center of the bull's-eye pattern. Cross correlation can be performed to automatically track the positions of markers reconstructed from adjacent rings of k-space. To increase the marker signal, the markers are encased in inductively coupled RF coils. Rigid-body motion in the yz-plane is calculated directly with the Euclidean group for rotation and translation, and corrected by rotating and applying phase shifts to any corrupted rings of data. In the current work we present a theoretical analysis of this method, as well as results of volunteer and controlled phantom experiments that demonstrate its initial feasibility. Although the EC view order has mainly been used for MR angiography (MRA), it can also be used for most 3D acquisitions.

Retrospective intra-scan motion correction

This paper analyzes the effects of intra-scan motion and demonstrates the possibility of correcting them directly in k-space with a new automatic retrospective method. The method is presented for series of 2D acquisitions with Cartesian sampling. Using a reference k-space acquisition (corrected for translations) within the series, intra-scan motion parameters are accurately estimated for each trajectory in k-space of each data set in the series resulting in pseudo-random sample positions. The images are reconstructed with a Bayesian estimator that can handle sparse arbitrary sampling in k-space and reduces intra-scan rotation artefacts to the noise level. The method has been assessed by means of a Monte Carlo study on axial brain images for different signal-to-noise ratios. The accuracy of motion estimates is better than 0.1 degrees for rotation, and 0.1 and 0.05 pixel, respectively, for translation along the read and phase directions for signal-to-noise ratios higher than 6 of the signals on each trajectory. An example of reconstruction from experimental data corrupted by head motion is also given.

The LONI Pipeline Processing Environment

The analysis of raw data in neuroimaging has become a computationally entrenched process with many intricate steps run on increasingly larger datasets. Many software packages exist that provide either complete analyses or specific steps in an analysis. These packages often possess diverse input and output requirements, utilize different file formats, run in particular environments, and have limited abilities with certain types of data. The combination of these packages to achieve more sensitive and accurate results has become a common tactic in brain mapping studies but requires much work to ensure valid interoperation between programs. The handling, organization, and storage of intermediate data can prove difficult as well. The LONI Pipeline Processing Environment is a simple, efficient, and distributed computing solution to these problems enabling software inclusion from different laboratories in different environments. It is used here to derive a T1-weighted MRI atlas of the human brain from 452 normal young adult subjects with fully automated processing. The LONI Pipeline Processing Environment's parallel processing efficiency using an integrated client/server dataflow model was 80.9% when running the atlas generation pipeline from a PC client (Acer TravelMate 340T) on 48 dedicated server processors (Silicon Graphics Inc. Origin 3000). The environment was 97.5% efficient when the same analysis was run on eight dedicated processors.

Prospective acquisition correction for head motion with image-based tracking for real-time fMRI

In functional magnetic resonance imaging (fMRI) head motion can corrupt the signal changes induced by brain activation. This paper describes a novel technique called Prospective Acquisition CorrEction (PACE) for reducing motion-induced effects on magnetization history. Full three-dimensional rigid body estimation of head movement is obtained by image-based motion detection to a high level of accuracy. Adjustment of slice position and orientation, as well as regridding of residual volume to volume motion, is performed in real-time during data acquisition. Phantom experiments demonstrate a high level of consistency (translation < 40 microm; rotation < 0.05 degrees ) for detected motion parameters. In vivo experiments were carried out and they showed a significant decrease of variance between successively acquired datasets compared to retrospective correction algorithms.