二维稀疏信号的联合压缩感知方法研究

A Two Dimensional Signal Jointly Reconstruction Method Based on Compressive Sensing

传统的压缩感知理论主要考虑一维稀疏信号的感知和重构。当待处理信号是二维(2 dimension,2D)或多维时,若直接将信号向量化处理,会造成感知矩阵维度急剧变大,使得存储和后续的重构复杂度大大增加,同时重构性能下降。为实现对2D信号的高效感知和快速重构,本文首先构建一个针对2D信号的模拟信息转换(Analog-to-Information Conversion,AIC)感知框架,通过行、列同时感知的策略实现量测值获取,以达到降低量测值存储维度的目的;其次针对压缩采样后的量测数据,提出一种2D快速迭代收缩阈值算法(2D Fast Iterative Shrinkage-Thresholding Algorithm,2D-FISTA),并对该算法的基本迭代格式、收敛条件、参数选择以及算法收敛速度等问题进行了详细分析。仿真结果表明,所研究的算法可直接处理2D信号,具有重构速度快和存储量低等优势。

Traditional compressive sensing theories mainly consider sampling and reconstructing a 1 Dimensional（ 1D） signal. For a 2 dimensional（ 2D） signal,if reshaped into a vector,the required size of the sensing matrix becomes dramatically large,which increases the storage and computational complexity of reconstruction significantly. To efficiently sample and reconstruct 2D signals exhibiting sparsity in 2D separable dictionaries,we first construct an analog-to-information conversion（ AIC） frame to jointly sample 2D signals in column and row instead of vectoring,which requires much lower storage. Then a novel 2D fast iterative shrinkage-thresholding algorithm（ 2D-FISTA） is proposed. The basic iterate format,convergence,parameter choices of the 2D-FISTA are thoroughly analyzed. It is shown that the proposed method can handle2 D signals directly with much lower storage and computational complexity.