A HIGH-DIMENSIONAL INVERSE FRAME OPERATOR APPROXIMATION TECHNIQUE

作者：Song Guohui^*; Davis Jacqueline; Gelb Anne

来源：SIAM Journal on Numerical Analysis, 2016, 54(4): 2282-2301.

DOI：10.1137/15M1047593

• inverse frame operator
• high-dimensional frames
• Fourier frames
• localized frames
• numerical frame approximation
• nonuniform Fourier data

The ability to efficiently and accurately approximate an inverse frame operator is critical for establishing the utility of numerical frame approximations. Recently, the admissible frame method was developed to approximate inverse frame operators for one-dimensional problems. Using the admissible frame approach, it is possible to project the corresponding frame data onto a more suitable (admissible) frame, even when the sampling frame is only weakly localized. As a result, a target function may be approximated as a finite frame expansion with its asymptotic convergence solely dependent on its smoothness. In this investigation, we seek to expand the admissible frame approach to higher dimensions, which requires some additional constraints. We prove that the admissible frame technique converges and then demonstrate its usefulness with some numerical experiments that use two-dimensional sampling patterns inspired by applications that acquire data nonuniformly in the Fourier domain.

• 出版日期2016