Sparse Solution of Underdetermined Linear Equations via Adaptively Iterative Thresholding

Finding the sparset solution of an underdetermined system of linear equations $y=Ax$ has attracted considerable attention in recent years. Among a large number of algorithms, iterative thresholding algorithms are recognized as one of the most efficient and important classes of algorithms. This is mainly due to their low computational complexities, especially for large scale applications. The aim of this paper is to provide guarantees on the global convergence of a wide class of iterative thresholding algorithms. Since the thresholds of the considered algorithms are set adaptively at each iteration, we call them adaptively iterative thresholding (AIT) algorithms. As the main result, we show that as long as $A$ satisfies a certain coherence property, AIT algorithms can find the correct support set within finite iterations, and then converge to the original sparse solution exponentially fast once the correct support set has been identified. Meanwhile, we also demonstrate that AIT algorithms are robust to the algorithmic parameters. In addition, it should be pointed out that most of the existing iterative thresholding algorithms such as hard, soft, half and smoothly clipped absolute deviation (SCAD) algorithms are included in the class of AIT algorithms studied in this paper.Comment: 33 pages, 1 figur

Self-Learning Hot Data Prediction: Where Echo State Network Meets NAND Flash Memories

© 2019 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.Well understanding the access behavior of hot data is significant for NAND flash memory due to its crucial impact on the efficiency of garbage collection (GC) and wear leveling (WL), which respectively dominate the performance and life span of SSD. Generally, both GC and WL rely greatly on the recognition accuracy of hot data identification (HDI). However, in this paper, the first time we propose a novel concept of hot data prediction (HDP), where the conventional HDI becomes unnecessary. First, we develop a hybrid optimized echo state network (HOESN), where sufficiently unbiased and continuously shrunk output weights are learnt by a sparse regression based on L2 and L1/2 regularization. Second, quantum-behaved particle swarm optimization (QPSO) is employed to compute reservoir parameters (i.e., global scaling factor, reservoir size, scaling coefficient and sparsity degree) for further improving prediction accuracy and reliability. Third, in the test on a chaotic benchmark (Rossler), the HOESN performs better than those of six recent state-of-the-art methods. Finally, simulation results about six typical metrics tested on five real disk workloads and on-chip experiment outcomes verified from an actual SSD prototype indicate that our HOESN-based HDP can reliably promote the access performance and endurance of NAND flash memories.Peer reviewe

Linear Convergence of Adaptively Iterative Thresholding Algorithms for Compressed Sensing

This paper studies the convergence of the adaptively iterative thresholding (AIT) algorithm for compressed sensing. We first introduce a generalized restricted isometry property (gRIP). Then we prove that the AIT algorithm converges to the original sparse solution at a linear rate under a certain gRIP condition in the noise free case. While in the noisy case, its convergence rate is also linear until attaining a certain error bound. Moreover, as by-products, we also provide some sufficient conditions for the convergence of the AIT algorithm based on the two well-known properties, i.e., the coherence property and the restricted isometry property (RIP), respectively. It should be pointed out that such two properties are special cases of gRIP. The solid improvements on the theoretical results are demonstrated and compared with the known results. Finally, we provide a series of simulations to verify the correctness of the theoretical assertions as well as the effectiveness of the AIT algorithm.Comment: 15 pages, 5 figure