A method to reduce the Gibbs ringing artifact in MRI scans while keeping tissue boundary integrity

Archibald, Rick; Gelb, Anne

doi:10.1109/tmi.2002.1000255

Cited by 109 publications

(75 citation statements)

References 14 publications

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“…Determining edges from the regriddedĝ(l) should be easily accomplished using standard Fourier based edge detection methods such as in [13]. 3 However, this requires extra processing, which is costly in two dimensions. 3.…”

Section: Parameter Selection For Convolutional Gridding Edge Detectionmentioning

confidence: 99%

“…As predicted by the formulation of (30), the method is unable to detect edges that lie only in the horizontal or vertical direction. In previous investigations concerning edge detection in images from uniform Fourier data, it was found that the results were best when a line by line approach was used in each dimension and then combined to form an edge map, [2,3,8]. In the case of non-uniform sampling, this would mean that the convolutional gridding reconstruction would first have to be computed, and then the FFT used to generate uniform Fourier coefficients.…”

Section: Two Dimensional Convolutional Gridding Edge Detectionmentioning

confidence: 99%

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Edge Detection from Non-Uniform Fourier Data Using the Convolutional Gridding Algorithm

2014

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Detecting edges in images from a finite sampling of Fourier data is important in a variety of applications. For example, internal edge information can be used to identify tissue boundaries of the brain in a magnetic resonance imaging (MRI) scan, which is an essential part of clinical diagnosis. Likewise, it can also be used to identify targets from synthetic aperture radar (SAR) data. Edge information is also critical in determining regions of smoothness so that high resolution reconstruction algorithms, i.e. those that do not "smear over" the internal boundaries of an image, can be applied. In some applications, such as MRI, the sampling patterns may be designed to oversample the low frequency while more sparsely sampling the high frequency modes. This type of non-uniform sampling creates additional difficulties in processing the image. In particular, there is no fast reconstruction algorithm, since the FFT is not applicable. However, interpolating such highly non-uniform Fourier data to the uniform coefficients (so that the FFT can be employed) may introduce large errors in the high frequency modes, which is especially problematic for edge detection. Convolutional gridding, also referred to as the non-uniform FFT (NFFT), is a forward method that uses a convolution process to obtain uniform Fourier data so that the FFT can be directly applied to recover the underlying image. Carefully chosen parameters ensure that the algorithm retains accuracy in the high frequency coefficients. Similarly, the convolutional gridding edge detection algorithm developed in this paper provides an efficient and robust way to calculate edges. We demonstrate our technique in one and two dimensional examples.

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Section: Parameter Selection For Convolutional Gridding Edge Detectionmentioning

confidence: 99%

Section: Two Dimensional Convolutional Gridding Edge Detectionmentioning

confidence: 99%

Edge Detection from Non-Uniform Fourier Data Using the Convolutional Gridding Algorithm

2014

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“…Previous studies, such as [2,3,20] have shown the effectiveness of performing Gegenbauer reconstructions on two-dimensional images, defined, of course, on evenly spaced grid points. In such cases the source data was understood to be from frequency space and hence, one-dimensional Fourier-Gegenbauer reconstructions were performed on each vertical column, or horizontal row, of data.…”

Section: Two-dimensional Reconstructionmentioning

confidence: 99%

“…But in order to do this, we first need to know the locations of the discontinuities in each line of data. Since we are not aware of a method to locate the physical discontinuities from the Chebyshev coefficients, we used the concentration edge detector in Fourier space, as described in [3,6], to locate the intervals of smoothness. Subsequently we applied the Chebyshev-Gegenbauer method, dynamically choosing optimal parameters as described in the paragraph above, and also by [21].…”

Section: Two-dimensional Reconstructionmentioning

confidence: 99%

A New Strategy for Choosing the Chebyshev‐gegenbauer Parameters in a Reconstruction Based on Asymptotic Analysis

Jackiewicz

Park

2010

Mathematical Modelling and Analysis

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Abstract. The Gegenbauer reconstruction method, first proposed by Gottlieb et.al. in 1992, has been considered a useful technique for re-expanding finite series polynomial approximations while simultaneously avoiding Gibbs artifacts. Since its introduction many studies have analyzed the method's strengths and weaknesses as well as suggesting several applications. However, until recently no attempts were made to optimize the reconstruction parameters, whose careful selection can make the difference between spectral accuracies and divergent error bounds. In this paper we propose asymptotic analysis as a method for locating the optimal Gegenbauer reconstruction parameters. Such parameters are useful to applications of this reconstruction method that either seek to bound the number of Gegenbauer expansion coefficients or to control compression ratios. We then illustrate the effectiveness of our approach with the results from some numerical experiments.

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“…At this point, the application of the enhancement procedure introduced in [8] works directly to pinpoint the jump discontinuities, without having to determine a neighborhood parameter (N). Furthermore, one can apply the minimization algorithm discussed in [1] and [2] to reduce the O(∆x) error in the approximation of the amplitude of the jump discontinuity.…”

Section: Minmod Edge Detectionmentioning

confidence: 99%

Adaptive Edge Detectors for Piecewise Smooth Data Based on the Minmod Limiter

Gelb¹,

Tadmor²

2005

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We are concerned with the detection of edges-the location and amplitudes of jump discontinuities of piecewise smooth data realized in terms of its discrete grid values. We discuss the interplay between two approaches. One approach, realized in the physical space, is based on local differences and is typically limited to low-order of accuracy. An alternative approach developed in our previous work [Gelb and Tadmor, Appl. Comp. Harmonic Anal., 7, 101-135 (1999)] and realized in the dual Fourier space, is based on concentration factors; with a proper choice of concentration factors one can achieve higherorders-in fact in [Gelb and Tadmor, SIAM J. Numer. Anal., 38, 1389-1408(2001] we constructed exponentially accurate edge detectors. Since the stencil of these highly-accurate detectors is global, an outside threshold parameter is required to avoid oscillations in the immediate neighborhood of discontinuities. In this paper we introduce an adaptive edge detection procedure based on a cross-breading between the local and global detectors. This is achieved by using the minmod limiter to suppress spurious oscillations near discontinuities while retaining high-order accuracy away from the jumps. The resulting method provides a family of robust, parameter-free edge-detectors for piecewise smooth data. We conclude with a series of one-and two-dimensional simulations.

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A method to reduce the Gibbs ringing artifact in MRI scans while keeping tissue boundary integrity

Cited by 109 publications

References 14 publications

Edge Detection from Non-Uniform Fourier Data Using the Convolutional Gridding Algorithm

Edge Detection from Non-Uniform Fourier Data Using the Convolutional Gridding Algorithm

A New Strategy for Choosing the Chebyshev‐gegenbauer Parameters in a Reconstruction Based on Asymptotic Analysis

Adaptive Edge Detectors for Piecewise Smooth Data Based on the Minmod Limiter

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