Residual-weighted two-step iterative thresholding shrinkage (RW-TWIST) algorithm for image reconstruction

Ultrafast compressive sensing imaging requires reconstruction algorithms with low computational complexity and high-quality reconstruction performance. Currently, the traditional compressive sensing TWIST algorithm is sensitive to parameter selection and struggles to preserve high-order and detailed image information, often resulting in noise and edge blurring in the reconstructed images. This paper proposes a residual-weighted two-step iterative thresholding shrinkage (RW-TWIST) image reconstruction algorithm, which, by employing an improved two-step iterative algorithm (TWIST) under L1-norm constraints, achieves an adaptive optimization model for the constraints of the objective function. The method introduces a nonlinear factor for residual weighting and threshold constraints, enhancing the algorithm's ability to handle complex, high-order information and enabling adaptive sparse signal reconstruction based on image features and the observation matrix. Experimental results show that the improved algorithm increases the PSNR by 2 dB, reduces reconstruction time, decreases computational complexity, improves structural similarity, and exhibits a faster convergence rate and better recovery stability. Moreover, the algorithm performs better in preserving high-order detail information. Furthermore, this method has promising applications in ultrafast event frame recovery and ultrafast compressive sensing imaging, offering higher reconstruction accuracy compared to other common algorithms.