Accelerating monotone fast iterative shrinkage-thresholding algorithm with sequential subspace optimization for sparse recovery

作者：Zhu, Tao^*

来源：Signal Image and Video Processing, 2020, 14(4): 771-780.

DOI：10.1007/s11760-019-01603-4

• Monotone fast iterative shrinkage-thresholding algorithm
• Acceleration
• Sequential subspace optimization
• Sparse recovery

The present paper focuses on accelerating monotone fast iterative shrinkage-thresholding algorithm (MFISTA) that is popular to solve the basis pursuit denoising problem for sparse recovery. Inspired by a recent work that accelerates MFISTA with line search, we alternatively use a much more effective speed-up option, termed sequential subspace optimization. Furthermore, instead of manually setting the number of previous propagation directions in the subspace beforehand, we propose an adaptive method to set it. Additionally, for approximating the absolute value function, we analyze the superiority of a smooth version used in this paper over the one recommended in a previous work, and give an analytical closed-form expression for the shrinkage operator corresponding to the smooth approximation. The experiments presented here show that the proposed method achieves faster convergence speeds in terms of iteration and run-time.