Recently, many new challenges in Compressed Sensing (CS), such as block sparsity, arose. In this paper, we present a new algorithm for solving CS with block sparse constraints (BSC) in complex fields. Firstly, based on block sparsity characteristics, we propose a new model to deal with CS with BSC and analyze the properties of the functions involved in this model. We then present a new $\tau$-stationary point and analyze corresponding first-order sufficient and necessary conditions. That ensures we to further develop a block Newton hard-thresholding pursuit (BNHTP) algorithm for efficiently solving CS with BSC. Finally, preliminary numerical experiments demonstrate that the BNHTP algorithm has superior performance in terms of recovery accuracy and calculation time when compared with the classical AMP algorithm.

翻译：最近,在压缩遥感(CS)中出现了许多新的挑战,例如块块宽度。在本文中,我们提出了一个新的算法,以在复杂领域以块小限制(BSC)解决块小限制(BSC)解决块小限制(CS)。首先,基于块宽度特点,我们提出了一个新的模型,以处理块宽度特点(CS),并分析该模型所涉功能的特性。然后我们提出一个新的美元固定点,并分析相应的一级足够和必要的条件。这确保了我们进一步发展一个块牛顿硬藏量追踪(BNHTP)算法(BNHTP),以便有效地与 BSC 解决 CS 。最后,初步数字实验表明,BNHTP算法在回收准确性和计算时间方面表现优异于传统的 AMP算法。