Fast matching pursuit with a multiscale dictionary of Gaussian chirps
Fast matching pursuit with a multiscale dictionary of Gaussian chirps
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DOI：
10.1109/78.917803
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发表时间：
2001-05-01
影响因子：
5.4
通讯作者：
Gribonval, R
中科院分区：
文献类型：
--
作者：
Gribonval, R
我们引入一种改进的匹配追踪算法，称为快速脊追踪，以计算复杂度$O(MN)$（而非预期的$O(MN^2\log N)$）用$M$个高斯线性调频信号来逼近$N$维信号。在追踪的每次迭代中，首先选择最佳的伽柏原子，然后对其尺度和调频斜率进行局部优化，以得到一个“良好”的线性调频原子，即与残差的相关性在局部达到最大的原子。证明了高斯线性调频字典的一个脊定理，由此构建了局部最优尺度和调频斜率的估计。该过程被限制在高斯伽柏字典的局部极大值子字典中，以进一步加速追踪。该方法的效率和速度在一个声音信号上得到了验证。
We introduce a modified matching pursuit algorithm, called fast ridge pursuit, to approximate N-dimensional signals with M Gaussian chirps at a computational cost O(MN) instead of the expected O(MN2 log N). At each iteration of the pursuit, the best Gabor atom is first selected, and then, its scale and chirp rate are locally optimized so as to get a "good" chirp atom, i.e., one for which the correlation with the residual is locally maximized. A ridge theorem of the Gaussian chirp dictionary is proved, from which an estimate of the locally optimal scale and chirp is built. The procedure is restricted to a sub-dictionary of local maxima of the Gaussian Gabor dictionary to accelerate the pursuit further. The efficiency and speed of the method is demonstrated on a sound signal.