Abstract
In the processing process of high-dimensional data, it is of great significance to identify the singularity of high-dimensional square integrable functions, which can be used as foundation of pattern recognition, data mining, spectrum analysis, fault diagnosis of large machinery, aerospace, remote sensing and control as well as the 3D image processing. Firstly, in the paper, the reconstruction formula of high-dimensional square integrable functions is given by using the continuous shearlet transform; secondly, the decay property of shearlet coefficients of several special functions is studied; finally, the singular support of square integrable functions is characterized by using the shearlet coefficients of reconstruction formula. Our results improve some known ones given by Kutyniok and Dahlke, et al.
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