Sparse Signal Reconstruction Based on Multiparameter Approximation Function with Smoothed l

The smoothed l0 norm algorithm is a reconstruction algorithm in compressive sensing based on approximate smoothed l0 norm. It introduces a sequence of smoothed functions to approximate the l0 norm and approaches the solution using the specific iteration process with the steepest method. In order to choose an appropriate sequence of smoothed function and solve the optimization problem effectively, we employ approximate hyperbolic tangent multiparameter function as the approximation to the big “steep nature” in l0 norm. Simultaneously, we propose an algorithm based on minimizing a reweighted approximate l0 norm in the null space of the measurement matrix. The unconstrained optimization involved is performed by using a modified quasi-Newton algorithm. The numerical simulation results show that the proposed algorithms yield improved signal reconstruction quality and performance

Two Regularization Models for Computed Tomography Image Reconstruction from Limited Projection Data

Computed tomography (CT) has been widely applied in medical imaging and industry for over decades. CT reconstruction from limited projection data is of particular importance. The total variation or l1-norm regularization has been widely used for image reconstruction in computed tomography (CT). Images in computed tomography (CT) are mostly piece-wise constant so the gradient images are considered as sparse images. The l0-norm of the gradients of an image provides a measurement of the sparsity of gradients of the image. However, the l0-norm regularization problem is NP hard. In this talk, we present two new models for CT image reconstruction from limited-angle projections. In one model we propose the smoothed l0-norm and l1-norm regularization using the nonmonotone alternating direction algorithm. In the other model we propose a combined l1-norm and l0-norm regularization model for better edge preserving

Enhanced Compressive Wideband Frequency Spectrum Sensing for Dynamic Spectrum Access

Wideband spectrum sensing detects the unused spectrum holes for dynamic spectrum access (DSA). Too high sampling rate is the main problem. Compressive sensing (CS) can reconstruct sparse signal with much fewer randomized samples than Nyquist sampling with high probability. Since survey shows that the monitored signal is sparse in frequency domain, CS can deal with the sampling burden. Random samples can be obtained by the analog-to-information converter. Signal recovery can be formulated as an L0 norm minimization and a linear measurement fitting constraint. In DSA, the static spectrum allocation of primary radios means the bounds between different types of primary radios are known in advance. To incorporate this a priori information, we divide the whole spectrum into subsections according to the spectrum allocation policy. In the new optimization model, the minimization of the L2 norm of each subsection is used to encourage the cluster distribution locally, while the L0 norm of the L2 norms is minimized to give sparse distribution globally. Because the L0/L2 optimization is not convex, an iteratively re-weighted L1/L2 optimization is proposed to approximate it. Simulations demonstrate the proposed method outperforms others in accuracy, denoising ability, etc.Comment: 23 pages, 6 figures, 4 table. arXiv admin note: substantial text overlap with arXiv:1005.180