An improved fast iterative shrinkage thresholding algorithm with an error for image deblurring problem

In this paper, we introduce a new iterative forward-backward splitting method with an error for solving the variational inclusion problem of the sum of two monotone operators in real Hilbert spaces. We suggest and analyze this method under some mild appropriate conditions imposed on the parameters such that another strong convergence theorem for these problem is obtained. We also apply our main result to improve the fast iterative shrinkage thresholding algorithm (IFISTA) with an error for solving the image deblurring problem. Finally, we provide numerical experiments to illustrate the convergence behavior and show the effectiveness of the sequence constructed by the inertial technique to the fast processing with high performance and the fast convergence with good performance of IFISTA.

Compressed Sensing Reconstruction of Radar Echo Signal Based on Fractional Fourier Transform and Improved Fast Iterative Shrinkage-Thresholding Algorithm

The compressed sensing theory, which has received great attention in the field of radar technology, can effectively reduce the data rate of high-resolution radar imaging systems and solve the problem of collecting, storing, and transmitting large amounts of data in radar systems. Through the study of radar signal processing theory, it can be found that the echo of radar LFM transmit signal has sparse characteristics in the distance upward; based on this, we can consider using the theory of compressed sensing in the processing of radar echo to optimize the processing. In this paper, a fast iterative shrinkage-thresholding reconstruction algorithm based on protection coefficients is proposed. Under the new scheme, firstly, the LFM echo signal’s good sparse representation is obtained by using the time-frequency sparse characteristics of the LFM echo signal under the fractional Fourier transform; all reconstruction coefficients are analyzed in the iterative process. Then, the coefficients related to the feature will be protected from threshold shrinkage to reduce information loss. Finally, the effectiveness of the proposed method is verified through simulation experiments and application example analysis. The experimental results show that the reconstruction error of this method is lower and the reconstruction effect is better compared with the existing reconstruction algorithms.

An Improved the Fast Iterative Shrinkage Thresholding Algorithm With an Error for Image Deblurring Problem

In this paper, we introduce a new iterative forward-backward splitting method with an error for solving the variational inclusion problem of the sum of two monotone operators in real Hilbert spaces. We suggest and analyze this method under some mild appropriate conditions imposed on the parameters such that another strong convergence theorem for these problem is obtained. We also apply our main result to improved the fast iterative shrinkage thresholding algorithm (IFISTA) with an error for solving the image deblurring problem. Finally, we provide numerical experiments to illustrate the convergence behavior and show the effectiveness of the sequence constructed by the inertial technique to the fast processing with high performance and the fast convergence with good performance of IFISTA.