Nonstandard Wavelet Decomposition of the Convolution and the Derivative Operators
نویسنده
چکیده
We describe numerical implementations of the discrete convolution operator and the derivative operator in the framework of nonstandard wavelet decomposition of linear operators. In both cases, the operator matrix and the input vector are rst expanded in a compactly supported discrete wavelet basis. Then the scale-wise eeect of the expanded operator matrix on the input vector is computed. The contributions from the various scales in the matrix-vector product are summed to yield the nal answer. There are two obvious advantages to this method. Firstly, it is possible to trade oo computational speed against the accuracy of the computation by thresholding the values of the wavelet expansion of the operator matrix. Secondly, the contributions of the operator from the various scales can be weighted to enhance/suppress certain scales.
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