压缩感知的等效二维稀疏变换

Equivalent Two-dimensional Sparse Transform of Compressive Sensing

目前的压缩感知研究尚不能真正实现基于二维稀疏变换的影像采集和重构。通过对二维压缩感知和稀疏变换的理论分析和数学推导,将基于一维稀疏变换的二维压缩感知模型等价转换成适用于二维稀疏变换的二维压缩感知模型。从而在测量过程不变的前提下,基于一维线阵推扫数据采集方式实现了基于二维稀疏变换的压缩感知影像采集和重构。实验验证了等效二维稀疏变换的正确性。

Based on theoretical analysis and mathematical deduction of two-dimensional compressed sensing and sparse transform,two-dimensional compressed sensing model based on one-dimensional sparse transform is equivalently converted into two-dimensional compressed sensing model for two-dimensional sparse transform.Thus on the premise of unchanging measurement process,compressed sensing image acquisition and reconstruction based on twodimensional sparse transform are implemented based on one-dimensional linear array push-broom data collection methods.Experiments verify the correctness of equivalent two-dimensional sparse transform.