We study Sparse Signal Recovery (SSR) methods for multichannel imaging with compressed {forward and backward} operators that preserve reconstruction accuracy. We propose a Compressed Block-Convolutional (C-BC) measurement model based on a low-rank Convolutional Neural Network (CNN) decomposition that is analytically initialized from a low-rank factorization of physics-derived forward/backward operators in time delay-based measurements. We use Orthogonal Matching Pursuit (OMP) to select a compact set of basis filters from the analytic model and compute linear mixing coefficients to approximate the full model. We consider the Learned Iterative Shrinkage-Thresholding Algorithm (LISTA) network as a representative example for which the C-BC-LISTA extension is presented. In simulated multichannel ultrasound imaging across multiple Signal-to-Noise Ratios (SNRs), C-BC-LISTA requires substantially fewer parameters and smaller model size than other state-of-the-art (SOTA) methods while improving reconstruction accuracy. In ablations over OMP, Singular Value Decomposition (SVD)-based, and random initializations, OMP-initialized structured compression performs best, yielding the most efficient training and the best performance.

翻译：本文研究了多通道成像中的稀疏信号恢复方法，该方法采用压缩的前向与后向算子，同时保持重建精度。我们提出了一种基于低秩卷积神经网络分解的压缩块卷积测量模型，该模型通过解析方式初始化，其初始化源于基于时间延迟测量的物理推导前向/后向算子的低秩分解。我们使用正交匹配追踪从该解析模型中选择一组紧凑的基滤波器，并计算线性混合系数以近似完整模型。我们将学习型迭代收缩阈值算法网络作为一个代表性示例，并提出了其C-BC-LISTA扩展。在多个信噪比下的模拟多通道超声成像实验中，C-BC-LISTA所需的参数量显著少于其他最先进方法，模型尺寸更小，同时提高了重建精度。在对正交匹配追踪初始化、基于奇异值分解的初始化以及随机初始化的消融实验中，正交匹配追踪初始化的结构化压缩表现最佳，实现了最高效的训练和最优的性能。