Fourier Single-Pixel Imaging Edge Detection in Arbitrary Directions

The standard edge detection method via fourier single-pixel imaging encodes the scene with Fourier patterns modulated by Sobel operators, which can directly reconstruct the object edges instead of the complete scene. This method is only sensitive to horizontal and vertical edge, which is not conducive to obtaining detailed edges because a natural image always have a variety of edge directions. However, as the number of directions increases, the sampling rate should be higher to improve the quality of edges. To trade-off low sampling rate and detailed edges, we propose an adaptive orientation and sampling number method, which can collect proper high-frequency information within a limited number of samples to accommodate the uncertainty of natural target edge orientation by introducing an arbitrary directional Sobel operator with spectral radial correlation. The simulation results show that the method in this paper has the highest image signal-to-noise ratio compared with the other two methods at 5%, 10% and 25% sampling rates. And it can reconstruct the edges of the image in any direction with high quality and reduce the reconstruction noise with a limited number of samples.