用低秩卷积分解压缩多通道成像的信号恢复模型，提升精度同时减少参数量。
Compressed BC-LISTA via Low-Rank Convolutional Decomposition
- 基于物理模型的低秩分解，构造可解析初始化的压缩卷积测量模型。
- 在多信噪比模拟超声成像中，参数量显著减少且重建精度更优。
- 适合追求高效高精度信号恢复的多通道成像研究者使用。
我们研究多通道成像中稀疏信号恢复（SSR）方法，针对压缩的前向与后向算子，在保持重建精度的前提下提出一种基于低秩卷积神经网络（CNN）分解的压缩块卷积（C-BC）测量模型。该模型通过时延测量中物理导出的前向/后向算子的低秩分解进行解析初始化。采用正交匹配追踪（OMP）从解析模型中选取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。以学习迭代收缩阈值算法（LISTA）为例，提出C-BC-LISTA扩展。在多种信噪比下的模拟多通道超声成像实验中，C-BC-LISTA相比其他先进方法显著减少参数数量和模型规模，同时提升重建精度。在对比OMP、基于奇异值分解（SVD）及随机初始化的消融实验中，OMP初始化的结构化压缩表现最佳，实现最高效的训练与最优性能。
原文摘要 · Abstract (English)
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.
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