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A nonlinear acceleration method for iterative algorithms
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DOI：10.1016/j.sigpro.2019.107346.png)
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Abstract
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Iterative methods have led to better understanding and solving problems such as missing sampling, de convolution, inverse systems, and impulsive and Salt and Pepper noise removal problems. However, the challenges regarding the speed of convergence and or the accuracy of the answer still remain. In order to improve the existing iterative algorithms, a non-linear method is discussed in this paper. The mentioned method is analyzed from different aspects, including its convergence and its ability to accelerate recursive algorithms. We show that this method is capable of improving Iterative Method (IM) as a non-uniform sampling reconstruction algorithm and some other iterative sparse recovery algorithms such as Iterative Reweighted Least Squares (IRLS), Iterative Method with Adaptive Thresholding (IMAT), Smoothed l(0) (SL0) and Alternating Direction Method of Multipliers (ADMM) for solving LASSO problem family (including LASSO itself, LASSO-LSQR and Group-LASSO). It is also capable of both accelerating and stabilizing the well-known Chebyshev Acceleration (CA) method. Furthermore, the proposed algorithm can extend the stability range by reducing the sensitivity of iterative algorithms to the changes of adaptation rate. (C) 2019 Elsevier B.V. All rights reserved.
Keywords:
Non-Linear Acceleration
Iterative Methods
Sparse Recovery
Acceleration Methods
IMAT
LASSO
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