Abstract
We investigate the split variational inclusion problem in Hilbert spaces. We propose efficient algorithms in which, in each iteration, the stepsize is chosen self-adaptive, and proves weak and strong convergence theorems. We provide numerical experiments to validate the theoretical results for solving the split variational inclusion problem as well as the comparison to algorithms defined by Byrne et al. and Chuang, respectively. It is shown that the proposed algorithms outrun other algorithms via numerical experiments. As applications, we apply our method to compressed sensing in signal recovery. The proposed methods have as a main advantage that the computation of the Lipschitz constants for the gradient of functions is dropped in generating the sequences.
Highlights
We aim to find the approximate algorithms with a new step size which is self-adaptive for solving our split variational inclusion problem (SVIP) and prove its convergence
We study the split feasibility problem (SFP) that is to seek x ∗ ∈ H1 such that x ∗ ∈ C and Ax ∗ ∈ Q, (53)
The observed data y is generated by white Gaussian noise with signal-to-noise ratio (SNR)40
Summary
Let H1 and H2 be infinite dimensional Hilbert spaces, A : H1 → H2 be a bounded and linear operator. Let H1 and H2 be two real Hilbert spaces, A : H1 → H2 be a bounded and linear operator. We obtain the result for split feasibility problem (SFP) and its applications to compressed sensing in signal recovery It reveals that our methods have a better convergence than those of Byrne et al [6] and Chuang [10,11]
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