Efficient $ell_q$ Minimization Algorithms for Compressive Sensing Based on Proximity Operator

This paper considers solving the unconstrained $ell_q$-norm ($0leq q<1$) regularized least squares ($ell_q$-LS) problem for recovering sparse signals in compressive sensing. We propose two highly efficient first-order algorithms via incorporating theproximity operator for nonconvex $ell_q$-norm functions into the fast iterative shrinkage/thresholding (FISTA) and the alternative direction method of multipliers (ADMM) frameworks, respectively. Furthermore, in solving the nonconvex $ell_q$-LS problem, a sequential minimization strategy is adopted in the new algorithms to gain better global convergence performance. Unlike most existing $ell_q$-minimization algorithms, the new algorithms solve the $ell_q$-minimization problem without smoothing (approximating) the $ell_q$-norm. Meanwhile, the new algorithms scale well for large-scale problems, as often encountered in image processing. We show that the proposed algorithms are the fastest methods in solving the nonconvex $ell_q$-minimization problem, while offering competent performance in recovering sparse signals and compressible images compared with several state-of-the-art algorithms.

Data Acquisition and Control System for Broad-band Microwave Reflectometry on EAST

Microwave reflectometry is a non-intrusive plasma diagnostic tool which is widely applied in many fusion devices. In 2014, the microwave reflectometry on Experimental Advanced Superconducting Tokamak (EAST) had been upgraded to measure plasma densityprofile and fluctuation, which covered the frequency range of Q-band (32-56 GHz), V-band (47-76 GHz) and W-band (71-110 GHz). This paper presented a dedicated data acquisition and control system (DAQC) to meet the measurement requirements of high accuracy and temporal resolution. The DAQC consisted of two control modules, which integrated arbitrary waveform generation block (AWG) and trigger processing block (TP), and two data acquisition modules (DAQ) that was implemented base on the PXIe platform from National Instruments (NI). All the performance parameters had satisfied the requirements of reflectometry. The actual performance will be further examined in the experiments of EAST in 2014.