IEEE Trans Biomed Eng. 2013 Oct;60(10):2794-805. doi: 10.1109/TBME.2013.2264772. Epub 2013 May 23.
Compressive sensing has shown significant promise in biomedical fields. It reconstructs a signal from sub-Nyquist random linear measurements. Classical methods only exploit the sparsity in one domain. A lot of biomedical signals have additional structures, such as multi-sparsity in different domains, piecewise smoothness, low rank, etc. We propose a framework to exploit all the available structure information. A new convex programming problem is generated with multiple convex structure-inducing constraints and the linear measurement fitting constraint. With additional a priori information for solving the underdetermined system, the signal recovery performance can be improved. In numerical experiments, we compare the proposed method with classical methods. Both simulated data and real-life biomedical data are used. Results show that the newly proposed method achieves better reconstruction accuracy performance in term of both L1 and L2 errors.
压缩感知在生物医学领域显示出了巨大的潜力。它可以从亚奈奎斯特随机线性测量中重建信号。经典方法仅在一个域中利用稀疏性。许多生物医学信号具有其他结构，例如不同域中的多稀疏性、分段平滑性、低秩等。我们提出了一种利用所有可用结构信息的框架。生成了一个具有多个凸结构诱导约束和线性测量拟合约束的新凸规划问题。通过添加用于解决欠定系统的额外先验信息，可以提高信号恢复性能。在数值实验中，我们将所提出的方法与经典方法进行了比较。使用了模拟数据和实际的生物医学数据。结果表明，新提出的方法在 L1 和 L2 误差方面都能实现更好的重建准确性。
