Restricted isometry constant improvement based on a singular value decomposition-weighted measurement matrix for compressed sensing

In compressed sensing, an exact reconstruction depends on the restricted isometry property with a small restricted isometry constant (RIC). Based on singular value decomposition (SVD), the authors improve the RICs of measurement matrices. The proposed weighted measurement matrix method breaks the limit to attain a small RIC and has potential applications in imaging systems. They derive an improvement sufficient condition for the RIC for exact reconstruction using the orthogonal matching pursuit algorithm. The numerical stability of the SVD-based weighted equation is analysed. Simulation results show that the reconstruction results obtained by the proposed SVD-based weighted approach are obviously better than those obtained by the direct reconstruction. In the simulation, they also successfully apply the proposed weighted equation for a computed tomography reconstruction.