Efficient sparse Fourier single-pixel imaging

Fourier single-pixel imaging (FSI) acquisition time is tied to the number of modulations. FSI has a tradeoff between efficiency and accuracy. This work reports a mathematical analytic tool for efficient sparse FSI sampling. It is an efficient and adjustable sampling strategy to capture more information about scenes with reduced modulation times. Specifically, we first conduct the statistical importance ranking of Fourier coefficients of natural images. We design a sparse sampling strategy for FSI with a polynomially decent probability of the ranking. The sparsity of the captured Fourier spectrum can be adjusted by altering the polynomial order. We utilize a compressive sensing (CS) algorithm for sparse FSI reconstruction. From quantitative results, we have obtained the experiential rules of optimal sparsity for FSI under different noise levels and at different sampling ratios.