Dept. of Electr. Eng., Stanford Univ., CA.
IEEE Trans Med Imaging. 1995;14(3):487-97. doi: 10.1109/42.414614.
A spectral extrapolation algorithm for spatially bounded images is presented. An image is said to be spatially bounded when it is confined to a closed region and is surrounded by a background of zeros. With prior knowledge of the spatial domain zeros, the extrapolation algorithm extends the image's spectrum beyond a known interval of low-frequency components. The result, which is referred to as the finite support solution, has space variant resolution; features near the edge of the support region are better resolved than those in the center. The resolution of the finite support solution is discussed as a function of the number of known spatial zeros and known spectral components. A regularized version of the finite support solution is included for handling the case where the known spectral components are noisy. For both the noiseless and noisy cases, the resolution of the finite support solution is measured in terms of its impulse response characteristics, and compared to the resolution of the zerofilled and Nyquist solutions. The finite support solution is superior to the zerofilled solution for both the noisy and noiseless data cases. When compared to the Nyquist solution, the finite support solution may be preferred in the noisy data case. Examples using medical image data are provided.
提出了一种用于有界空间图像的谱外推算法。当图像被限制在一个封闭区域内并且被零值背景包围时，就称其为有界空间图像。利用空间域零值的先验知识，外推算法将图像的频谱扩展到已知低频分量的间隔之外。该结果被称为有限支撑解，具有空间变化的分辨率；支撑区域边缘附近的特征比中心的特征分辨率更高。有限支撑解的分辨率作为已知空间零值和已知谱分量数量的函数进行讨论。还包括有限支撑解的正则化版本，用于处理已知谱分量有噪声的情况。对于无噪声和有噪声两种情况，都根据其冲激响应特性来衡量有限支撑解的分辨率，并与零填充解和奈奎斯特解的分辨率进行比较。对于有噪声和无噪声两种数据情况，有限支撑解都优于零填充解。与奈奎斯特解相比，在有噪声数据情况下，有限支撑解可能更受欢迎。提供了使用医学图像数据的示例。
