Dept. of Comput. Sci., Massachusetts Univ., Lowell, MA.
IEEE Trans Image Process. 1993;2(2):152-9. doi: 10.1109/83.217220.
Properties of the Gabor transformation used for image representation are discussed. The properties can be expressed in matrix notation, and the complete Gabor coefficients can be found by multiplying the inverse of the Gabor (1946) matrix and the signal vector. The Gabor matrix can be decomposed into the product of a sparse constant complex matrix and another sparse matrix that depends only on the window function. A fast algorithm is suggested to compute the inverse of the window function matrix, enabling discrete signals to be transformed into generalized nonorthogonal Gabor representations efficiently. A comparison is made between this method and the analytical method. The relation between the window function matrix and the biorthogonal functions is demonstrated. A numerical computation method for the biorthogonal functions is proposed.
讨论了用于图像表示的 Gabor 变换的性质。这些性质可以用矩阵符号表示，并且可以通过将 Gabor（1946）矩阵的逆乘以信号向量来找到完整的 Gabor 系数。Gabor 矩阵可以分解为稀疏常数复矩阵和仅依赖于窗口函数的另一个稀疏矩阵的乘积。建议了一种快速算法来计算窗口函数矩阵的逆，从而可以有效地将离散信号转换为广义非正交 Gabor 表示。比较了这种方法和解析方法。演示了窗口函数矩阵和双正交函数之间的关系。提出了双正交函数的数值计算方法。
