Enhancing Single-Pixel Imaging by Balancing Wavelet Coefficients Weight with an Exponentially Increasing Diagonal Matrix

Optimizing the sparse basis is an effective way to enhance single-pixel imaging performance. Compressed sensing typically employs discrete wavelet basis to map signals into the wavelet domain to achieve approximate sparsity, where wavelet coefficients resemble an exponential decay form. However, in the penalty term of cost function, large lowfrequency wavelet coefficients carry higher weights, while the weights assigned to small high-frequency coefficients are much smaller. This implies that high-frequency coefficients are easily neglected in optimization and are even mistaken as noise and removed, resulting in the loss of image details.We propose an effective method that introduces a diagonal matrix W with exponentially increasing diagonal elements to balance the weights of low-frequency and high-frequency wavelet coefficients, ensuring the weights of high-frequency coefficients are ample to prevent them from being mistakenly treated as noise and discarded.For normalized images of size 256*256 with 25% sampling, proposed method are applied to several common compressed sensing algorithms for single-pixel imaging reconstruction such as L1-minimization, LASSO, and OMP. The simulation results indicate an average improvement of 1.10dB, 1.32dB, and 2.65dB in PSNR, respectively. Even in the presence of strong Gaussian noise with σ =0.2, the method can still partly enhance reconstruction performance.This research provides a novel perspective on optimizing the sparse basis and a practical approach to improving single-pixel imaging performance.