Two-stage adaptive random Fourier sampling method for image reconstruction

作者：

Highlights：

• We discover a column-wise maximum coherent structure in the Fourier-Haar interplay.

• A few examples of exact recovery of the Haar wavelet coefficients of an image are provided in a constrained ℓ1 minimization with a small number of high magnitude Fourier samples based on the maximum coherent structure.

• A two-stage adaptive Fourier sampling scheme is proposed to acquire such a small number of meaningful Fourier samples supported by the exact recovery examples.

• The proposed sampling scheme is confirmed to reveal high frequency patterns better than other well-known efficient sampling schemes, showing its numerical superiority in the ℓ1 minimization.

摘要

•We discover a column-wise maximum coherent structure in the Fourier-Haar interplay.•A few examples of exact recovery of the Haar wavelet coefficients of an image are provided in a constrained ℓ1 minimization with a small number of high magnitude Fourier samples based on the maximum coherent structure.•A two-stage adaptive Fourier sampling scheme is proposed to acquire such a small number of meaningful Fourier samples supported by the exact recovery examples.•The proposed sampling scheme is confirmed to reveal high frequency patterns better than other well-known efficient sampling schemes, showing its numerical superiority in the ℓ1 minimization.

论文关键词：Image reconstruction,High magnitude Fourier samples,Variable density random sampling,Constrained ℓ1 minimization

论文评审过程：Received 16 October 2020, Revised 19 February 2021, Accepted 4 April 2021, Available online 20 April 2021, Version of Record 20 April 2021.

论文官网地址：https://doi.org/10.1016/j.patcog.2021.107990