Dov Rosenfeld

Two-dimensional phase unwrapping using a minimum spanning tree algorithm

Phase unwrapping refers to the determination of phase from modulo 2pi data, some of which may not be reliable. In 2D, this is equivalent to confining the support of the phase function to one or more arbitrarily shaped regions. A phase unwrapping algorithm is presented which works for 2D data known only within a set of nonconnected regions with possibly nonconvex boundaries. The algorithm includes the following steps: segmentation to identify connectivity, phase unwrapping within each segment using a Taylor series expansion, phase unwrapping between disconnected segments along an optimum path, and filling of phase information voids. The optimum path for intersegment unwrapping is determined by a minimum spanning tree algorithm. Although the algorithm is applicable to any 2D data, the main application addressed is magnetic resonance imaging (MRI) where phase maps are useful.

Motion artifact correction in MRI using generalized projections

An algorithm that suppresses translational motion artifacts in magnetic resonance imaging (MRI) by using post processing on a standard spin-warp image is presented. It is shown that translational motion causes an additional phase factor in the detected signal and that this phase error can be removed using an iterative algorithm of generalized projections. The method has been tested using computer simulations and it successfully removed most of the artifact. The algorithm converges even in the presence of severe noise.

An improved algorithm for 2-D translational motion artifact correction

The quality of magnetic resonance imaging systems has improved to the point that motion is a major limitation in many examinations. Translational motion in the imaging plane causes the phase of the data to be corrupted. An algorithm using computer post-processing is proposed to correct the phase of the data, and hence remove the artifact. This algorithm has superior convergence properties to an earlier algorithm, which is achieved by incorporating additional prior information specific to the situation. The algorithm is verified using a Shepp and Logan phantom with simulated motion in the imaging plane. It is shown that the algorithm can correct both periodic and random motion, and that the algorithm is not significantly degraded when noise is present.

A modified Gerchberg-Saxton algorithm for one-dimensional motion artifact correction in MRI

A novel method for the suppression of one-dimensional translational motion artifacts in two-dimensional Fourier transform magnetic resonance images is presented. It is shown that the motion causes an additional phase factor in the detected signal and that this phase error can be removed using a modified Gerchberg-Saxton (1972) algorithm. The major differences between this algorithm and other phase retrieval algorithms are: (1) the phase information is not totally unavailable, but in a corrupted form; and (2) the algorithm does not try to recover the entire phase information from the magnitude of the detected signal, but rather to correct the distorted phase using the average phase error. The method has been successfully tested using computer simulations. >

Spin-Inversion Imaging: A Technique for NMR Imaging under Magnetic Fields with High Field Nonuniformities

An NMR imaging method, called spin invesion (SI) imaging, is described for imaging under a magnetic field with high nonuniformity. 180° flips are applied between sampling times of the FID to remove the effects of field nonuniformities on the FID. The only requirement for SI imaging is to have high enough RF power. This requirement may be satisfied safely for small volume imaging, for example, head scanning. The advantages of SI imaging are that the images produced are almost independent of the effects of main-field nonuniformities and chemical shifts, and that there is no stringent requirement on the gradient pulse shapes. In this paper, the technique is described, gradient and sampling period requirements are derived, methods for reducing the RF peak power needed are developed, and a computer simulation to demonstrate the technique is presented.

The application of spinors to solving the Bloch equations

Abstract In most cases the Bloch equations do not have an analytic solution. The mathematics of spinors are used in this paper to transform the Bloch equations, with the relaxation terms ignored, to two complex coupled differential equations. It is shown that this enables an analytic solution to be found for some particular situations of interest in NMR. As an example of this method, this paper treats the case where the Larmor frequency or the RF frequencies are changing linearly in time during excitation.

Fast Magnetic Resonance Imaging Using Spiral Trajectories

Acquisition times in magnetic resonance imaging (MRI) are typically in the order of minutes. For an image of 256 x 256 pixels, the standard Fourier reconstruction technique used in most commercial imaging systems requires 256 separate free induction decay (FID) signals. While the FID signal itself is of relatively short duration, the successive FID signals are separated by long delays, of the order of seconds, to permit substantial relaxation of the signal before the next excitation. The resultant long acquisition times give rise to motion artefacts, preclude dynamic imaging and keep the patient throughput low. In this paper, we investigate a fast imaging scheme which uses spiral trajectories in the spatial frequency domain. The entire domain can be sampled in a short time, requiring as few as one FID acquisition. The scheme requires time varying gradients having the form of a ramped sinusoid. Several reconstruction methods are considered for forming the image from the spatial frequency domain data. The possibility of using multiple spirals to deal with the rapid decay of the FID signal is also examined in detail.

Compression and reconstruction of MRI images using 2D DCT

In magnetic resonance imaging (MRI), the original data are sampled in the spatial frequency domain. The sampled data thus constitute a set of discrete Fourier transform (DFT) coefficients. The image is usually reconstructed by taking inverse DFT. The image data may then be compressed using the discrete cosine transform (DCT). We present here a method of treating the data that combines two procedures, image reconstruction and data compression. This method may be particularly useful in medical picture archiving and communication systems (PACS) where both image reconstruction and compression are important issues.

Resolution Enhancement In Ultrasonic Imaging By A Time-Varying Filter

The study reported here investigates the use of a time-varying filter to compensate for the spreading of ultrasonic pulses due to the frequency dependence of attenuation by tissues. The effect of this pulse spreading is to degrade progressively the axial resolution with increasing depth. The form of compensation required to correct for this effect is impossible to realize exactly. A novel time-varying filter utilizing a bank of bandpass filters is proposed as a realizable approximation of the required compensation. The performance of this filter is evaluated by means of a computer simulation. The limits of its application are discussed. Apart from improving the axial resolution, and hence the accuracy of axial measurements, the compensating filter could be used in implementing tissue characterization algorithms based on attenuation data.

Design And Construction Of SUMRIS -The Sydney University Magnetic Resonance Imaging System

A magnetic resonance imaging system for investigation and development of nuclear magnetic resonance (NMR) imaging techniques is being constructed by the NMR, Imaging Group within the School of Electrical Engineering at the University of Sydney. The system will also be capable of spatially-localized in-vivo spectroscopy. Primary requirements of a research instrument are flexibility and low cost, precluding purchase of a commercial system and necessitating in-house construction. The appropriate design strategy adopted was to start by building a simple NMR apparatus and expand it in steps, progressing towards a complete imaging and spectroscopy system.