Optimizing the quality of Fourier single-pixel imaging via generative adversarial network

Self-adaptive sampling for Fourier single-pixel imaging using probability estimation

“…FSI is more advantageous in terms of image energy concentration than HSI, especially under low sampling conditions. 20,21 Zhang et al 22 initially introduced the concept of SPI by utilizing Fourier spectrum acquisition. They subsequently proposed various sampling strategies, which refer to different arrangements of the Fourier basis patterns.…”

“…However, this approach can lead to the presence of ringing artifacts and blur in the reconstructed image I Ã due to the absence of high-frequency coefficients. 20,31 Variable density FSI suggests a sampling probability determined by the distance from the center of the Fourier spectrum, as shown in Eq. ( 6).…”

“…Pseudo-random patterns are commonly used in SPI, while deterministic patterns, such as Hadamard single-pixel imaging (HSI) and Fourier single-pixel imaging (FSI), have become popular more recently. FSI is more advantageous in terms of image energy concentration than HSI, especially under low sampling conditions 20 , 21 …”

“…In three-step FSI, with a fixed phase of Δϕ(i.e., 0,2π/3,4π/3), each Fourier coefficient can be acquired based on every three corresponding illumination patterns 20 . Each complex Fourier coefficient F(fx,fy) can therefore be obtained as F(fx,fy)=(2T0−T2π/3−T4π/3)+3j(T2π/3−T4π/3).…”

“…Consequently, only the low-frequency Fourier coefficients are acquired. However, this approach can lead to the presence of ringing artifacts and blur in the reconstructed image I* due to the absence of high-frequency coefficients 20 , 31 …”