Smoothed L0 Norm Algorithm Research Articles

Real Aperture Radar Angular Super-Resolution Imaging Using Modified Smoothed L0 Norm with a Regularization Strategy

Restricted by the ill-posed antenna measurement matrix, the conventional smoothed L0 norm algorithm (SL0) fails to enable direct real aperture radar angular super-resolution imaging. This paper proposes a modified smoothed L0 norm (MSL0) algorithm to address this issue. First, as the pseudo-inverse of the ill-posed antenna measurement matrix is required to set the initial values and calculate the gradient projection, a regularization strategy is employed to relax the ill-posedness. Based on the regularization strategy, the proposed MSL0 algorithm can avoid noise amplification when faced with the ill-posed antenna measurement matrix of real aperture radar. Additionally, to prevent local minima problems, we introduce a hard thresholding operator, based on which the proposed MSL0 algorithm can accurately reconstruct sparse targets. Simulations and experimental results verify the performance of the proposed MSL0 algorithm.

High-resolution imaging and micro-motion feature extraction of space multiple targets

In radar applications, different micro-motion forms can be used as the basis of target recognition. However, the radar echo signal of multiple spatial targets is overlapping in the time-frequency and time-range domains, which increases the difficulty of micro-motion feature extraction. In this paper, a high-resolution imaging and micro-motion feature extraction framework based on a multiple joint-domain radar tool is proposed to address this mixed signal. First, an accurate and suitable micro-motion model of cone-shaped space multiple targets is built. Then, the two-dimensional adaptive regularized smoothed L0 norm algorithm (2D AReSL0) based on sparse reconstruction is formulated to directly reconstruct the inverse synthetic aperture radar (ISAR) image. Additionally, the range-frequency-time radar data cube can be extracted from the ISAR movie by the CLEAN algorithm. To solve the scattering point association problem in the radar data cube, a 3D segmentation Viterbi algorithm is designed to extract the micro-motion features. Finally, simulation and experiment results demonstrate the effectiveness of the proposed framework.

Fast SL0 algorithm for 3D imaging using bistatic MIMO radar

Multiple-input-multiple-output (MIMO) radar is attractive in moving targets imaging, which is able to solve the difficulty of complex motion compensation. In this article, a three-dimensional imaging method using bistatic MIMO radar is proposed. Compared with monostatic MIMO radar, the bistatic system can provide the complementary information, and the imaging process is not the same as the monostatic case. Furthermore, considering the image sparsity and the spatial limitation of radar targets, a fast smoothed L0 norm algorithm is proposed to achieve the high resolution in cross-range directions with limited antennas. The experimental results demonstrate the validity and efficiency of the proposed method.

Regularized smoothed ℓ0 norm algorithm and its application to CS-based radar imaging

Sparse signal recovery is attractive in compressed sensing (CS). Based on the smoothed ℓ0 norm (SL0) algorithm, we have developed an error-tolerant regularized SL0 (ReSL0) algorithm, which has the same computational advantages as the SL0 algorithm while having better immunity against inaccuracy caused by noise or model mismatch. The performance of the ReSL0 is evaluated with simulated data. In addition, we have extended the ReSL0 to the matrix form (MReSL0), which is more suitable for dealing with matrix form signals and also has good resilience against inaccuracy. Finally we apply the ReSL0 and MReSL0 to joint CS-based radar imaging and phase error correction. Experimental results from both simulated and real data demonstrate that the proposed algorithms provide remarkable performance improvements in inaccurate scenarios (such as noisy data and mismatched settings) compared with the SL0 algorithm.

Image Reconstruction of Compressed Sensing Based on Improved Smoothed l0 Norm Algorithm

Image Reconstruction of Compressed Sensing Based on Improved Smoothed l0 Norm Algorithm

Improved smoothed L0 reconstruction algorithm for ISI sparse channel estimation

In this paper, the problem of inter symbol interference (ISI) sparse channel estimation in wireless communication with the application of compressed sensing is investigated. However, smoothed L0 norm algorithm (SL0) has ‘notched effect’ due to the negative iterative gradient direction. Moreover, the property of continuous function in SL0 is not steep enough, which results in inaccurate estimations and low convergence. Afterwards, we propose the Lagrange multipliers as well as Newton method to optimize SL0 algorithm in order to obtain a more rapid and efficient signal reconstruction algorithm, improved smoothed L0 (ISL0). ISI channel estimation will have a direct effect on the performance of ISI equalizer at the receiver. So, we design a pre-filter model which with no considerable loss of optimality and do analyses of the equalization methods of the sparse multi-path channel. Real-time simulation results clearly show that the ISL0 algorithm can estimate the ISI sparse channel much better in both signal noise ratio (SNR) and compression levels. In the same channel conditions, ISL0 algorithm has been greatly improved when compared with the SL0 algorithm and other compressed-sensing algorithms.

Sparse Signal Reconstruction Based on Multiparameter Approximation Function with Smoothedl0Norm

The smoothedl0norm algorithm is a reconstruction algorithm in compressive sensing based on approximate smoothedl0norm. It introduces a sequence of smoothed functions to approximate thel0norm 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” inl0norm. Simultaneously, we propose an algorithm based on minimizing a reweighted approximatel0norm 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.

Recovery of correlated row sparse signals using smoothed L0-norm algorithm

Distributed compressed sensing (DCS) is an emerging research field which exploits both intra-signal and inter-signal correlations. This paper focuses on the recovery of the sparse signals which can be modeled as joint sparsity model (JSM) 2 with different nonzero coefficients in the same location set. Smoothed L0 norm algorithm is utilized to convert a non-convex and intractable mixed L2,0 norm optimization problem into a solvable one. Compared with a series of single-measurement-vector problems, the proposed approach can obtain a better reconstruction performance by exploiting the inter-signal correlations. Simulation results show that our algorithm outperforms L1,1 norm optimization for both noiseless and noisy cases and is more robust against thermal noise compared with L1,2 recovery. Besides, with the help of the core concept of modified compressed sensing (CS) that utilizes partial known support as side information, we also extend this algorithm to decode correlated row sparse signals generated following JSM 1.