Abstract
Compressed sensing (CS) theory has attracted widespread attention in recent years and has been widely used in signal and image processing, such as underdetermined blind source separation (UBSS), magnetic resonance imaging (MRI), etc. As the main link of CS, the goal of sparse signal reconstruction is how to recover accurately and effectively the original signal from an underdetermined linear system of equations (ULSE). For this problem, we propose a new algorithm called the weighted regularized smoothed -norm minimization algorithm (WReSL0). Under the framework of this algorithm, we have done three things: (1) proposed a new smoothed function called the compound inverse proportional function (CIPF); (2) proposed a new weighted function; and (3) a new regularization form is derived and constructed. In this algorithm, the weighted function and the new smoothed function are combined as the sparsity-promoting object, and a new regularization form is derived and constructed to enhance de-noising performance. Performance simulation experiments on both the real signal and real images show that the proposed WReSL0 algorithm outperforms other popular approaches, such as SL0, BPDN, NSL0, and L-RLSand achieves better performances when it is used for UBSS.
Highlights
The problem that underdetermined blind source separation (UBSS) [1,2] needs to address is how to separate multiple signals from a small number of sensors
For signal recovery under noise conditions, we evaluate the performance of algorithms by the normalized mean squared error (NMSE) and the CPU running time (CRT)
We propose the weighted regularized smoothed L0-norm minimization algorithm (WReSL0) algorithm to recover the sparse signal from given
Summary
The objective function of these algorithms is given by: arg min x ∈Rn k Φx − yk 22 , s.t. k xk 0 ≤ K. the features of GMP algorithms can be concluded as: Using sparsity as prior information; Using the least squares error as the iterative criterion. Zhao proposed another smoothed function: the hyperbolic tangent (tanh) [20], f σ ( xi ) = This smoothed function makes a closer approximation to the L0 -norm than the Gauss function, as shown in [19], with the same σ; it performs better in sparse signal recovery. Compared to the L1 -norm, the nonconvex L p -norm to the pth power makes a closer approximation to the L0 -norm; L p -norm minimization has a better sparse recovery performance [8].
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