This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible. Numerous renowned algorithms for tackling the compressed sensing problem employ an alternating strategy, which typically involves data matching in one module and denoising in another. We present a novel approach, the Alternating Subspace Method (ASM), which integrates the principles of the greedy methods (e.g., the orthogonal matching pursuit type methods) and the splitting methods (e.g., the approximate message passing type methods). Crucially, ASM enhances the splitting method by achieving fidelity in a subspace-restricted fashion. \textcolor{black}{We reveal that such a restriction strategy guarantees global convergence via proximal residual control and establish its local geometric convergence on the LASSO problem.} Numerical experiments on the LASSO, channel estimation, and dynamic compressed sensing problems demonstrate its high convergence rate and its capacity to incorporate different prior distributions. Overall, the proposed method is promising in terms of efficiency, accuracy, and flexibility, and has the potential to be competitive in different sparse recovery applications.

翻译：本文已提交至IEEE考虑发表。版权可能未经通知即被转移，届时本版本可能无法访问。众多解决压缩感知问题的著名算法采用交替策略，通常包含一个模块进行数据匹配，另一个模块进行去噪。我们提出了一种新方法——交替子空间方法（ASM），该方法融合了贪婪方法（例如正交匹配追踪类方法）和分裂方法（例如近似消息传递类方法）的原理。关键在于，ASM通过以子空间限制的方式实现保真度，从而改进了分裂方法。\textcolor{black}{我们揭示了这种限制策略通过近端残差控制保证了全局收敛性，并在LASSO问题上建立了其局部几何收敛性。}在LASSO、信道估计和动态压缩感知问题上的数值实验证明了其高收敛率以及整合不同先验分布的能力。总体而言，所提方法在效率、准确性和灵活性方面前景广阔，并有望在不同的稀疏恢复应用中具备竞争力。