  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.
