基于Chebyshev多项式的消除Gibbs伪影的快速算法

冯前进; 黄鑫; 冯衍秋

doi:10.11834/jig.200608192

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基于Chebyshev多项式的消除Gibbs伪影的快速算法
A Fast Algorithm to Reduce Gibbs Ringing Artifact Based on the Chebyshev Polynomials
2006年11卷第8期页码：1132
纸质出版：2006
DOI： 10.11834/jig.200608192
稿件说明：

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冯前进, 黄鑫, 冯衍秋. 基于Chebyshev多项式的消除Gibbs伪影的快速算法[J]. 中国图象图形学报, 2006,11(8):1132. DOI： 10.11834/jig.200608192.

A Fast Algorithm to Reduce Gibbs Ringing Artifact Based on the Chebyshev Polynomials[J]. Journal of Image and Graphics, 2006, 11(8): 1132. DOI： 10.11834/jig.200608192.

摘要

在磁共振成像中通常通过减少相位编码次数来缩短数据采集时间，这样只能得到部分原始k空间数据，运用傅里叶变换成像时会在图像中产生常见的Gibbs环状伪影。Gegenbauer重建方法是一种能够有效消除Gibbs环状伪影并能保持高分辨率的图像重建方法，但是这种方法的缺点在于重建时间长且参数选择必须满足严格的限制且对图像重建质量影响较大。本文提出的基于Chebyshev多项式的逆多项式重建方法是针对Gegenbauer方法的改进算法，在改进原有算法不足的同时有效提高了重建精度。实验结果验证了该算法的有效性。

Abstract

In magnetic resonance imaging

the number of phase-encoded signals is often reduced to minimize the acquisition time.The partial k-space data lead to the famous Gibbs artifact with Fourier transform method.The Gegenbauer reconstruction method has been shown to effectively eliminate the Gibbs artifact and restore high resolution.However

the disadvantages of using the Gegenbauer method are more computational time

and more constrains

where parameters must satisfy certain conditions.The paper shows that the inverse polynomial reconstruction method(IPRM) based on Chebyshev polynomials effectively improves the Gegenbauer method and reduces reconstruction error.In this paper

we discuss IPRM based on Chebyshev polynomials and experimental results.The proposed method is verified with experiments of artifact removal.