A Single-Pixel Imaging Method Based on Compressed Sensing for Improvement of Image Quality

The image quality under single-pixel imaging method combined with compressed sensing theory is poor at low sampling rates. To solve this problem, we propose a new sparse matrix and a new imaging method. First, we construct truncated sparse wavelet transform basis based on discrete wavelet transform basis by using the construction method of sparse wavelet transform basis, so that the signal is represented more sparsely. After that, we optimize
$\ell _{1}$
-norm minimization algorithm by constructing an intermediate function so that the optimal solution of transformed problem is closer to the
$\ell _{0}$
-norm minimum solution. Simulation and experiment show that the proposed method increases peak signal-to-noise ratio and structural similarity of imaging results, effectively improving the image quality.