Mitchell D K, Nichols S T, Smith M R, Scott K
Department of Electrical Engineering, University of Calgary, Alberta, Canada.
Magn Reson Med. 1989 Mar;9(3):353-68. doi: 10.1002/mrm.1910090307.
Manipulation of the data describing two-dimensional magnetic resonance (MR) images can be used to zoom an image, decrease image noise and artifacts by modeling, or emphasize object edges in the field of view. In this paper, a two-dimensional band-selectable digital filtering (2D-BSDF) technique is detailed. This can be used to decrease the computational burden and increase algorithm stability associated with such data manipulation. Many display devices have the ability of expanding an image by pixel or linear interpolation. Application of the efficient zooming fast Fourier transformation algorithms provides a superior quality sinc-function interpolated image. In 2D-BSDF, the ideal rectangular windows used in sinc-function interpolation are replaced by windows with a more gradual roll-off. This gradual roll-off results in a slight degradation of the image edges but substantially reduces the computation time. Modeling of MRI data has been attempted to remove noise and artifacts from the image. These algorithms are computationally expensive and frequently unstable because of the high model orders required. The 2D-BSDF can be used to prepare a reduced data set, without loss of information. A lower order model may be applied to the subset and computation times approaching that required for normal fast Fourier transform algorithms result. The absence of noise and signal from objects outside the region of interest can considerably enhance the stability of the modeling algorithms. The use of BSDF is equally applicable when used in association with the modeling of 2D NMR spectroscopy data or with edge enhancement or any other data manipulation of magnetic resonance imaging images. In this paper an explanation of 1D-BSDF is provided and an algorithm for 2D-BSDF is developed. A comparison of filter designs and computational times is given when applying the technique to zooming and modeling of MR images. Images from medical MRI data are provided.
对描述二维磁共振（MR）图像的数据进行处理，可用于缩放图像、通过建模减少图像噪声和伪影，或增强视野中的物体边缘。本文详细介绍了一种二维带选数字滤波（2D-BSDF）技术。该技术可用于减轻与此类数据处理相关的计算负担，并提高算法稳定性。许多显示设备具有通过像素或线性插值来扩展图像的能力。高效缩放快速傅里叶变换算法的应用可提供高质量的 sinc 函数插值图像。在 2D-BSDF 中，sinc 函数插值中使用的理想矩形窗口被具有更平缓滚降特性的窗口所取代。这种平缓滚降会导致图像边缘略有退化，但可大幅减少计算时间。人们已尝试对 MRI 数据进行建模，以去除图像中的噪声和伪影。由于所需的模型阶数较高，这些算法计算成本高昂且常常不稳定。2D-BSDF 可用于准备一个精简数据集，而不会丢失信息。可以将较低阶的模型应用于该子集，从而得到接近普通快速傅里叶变换算法所需的计算时间。感兴趣区域之外的物体不存在噪声和信号，这可显著提高建模算法的稳定性。当与二维核磁共振波谱数据建模、边缘增强或磁共振成像图像的任何其他数据处理结合使用时，BSDF 的应用同样适用。本文提供了一维 BSDF 的解释，并开发了二维 BSDF 的算法。在将该技术应用于 MR 图像的缩放和建模时，给出了滤波器设计和计算时间的比较。还提供了来自医学 MRI 数据的图像。
