Extrapolated Proximal Subgradient Algorithms for Nonconvex and Nonsmooth Fractional Programs

In this paper, we consider a broad class of nonsmooth and nonconvex fractional programs, which encompass many important modern optimization problems arising from diverse areas such as the recently proposed scale-invariant sparse signal reconstruction problem in signal processing. We propose a proximal subgradient algorithm with extrapolations for solving this optimization model and show that the iterated sequence generated by the algorithm is bounded and that any one of its limit points is a stationary point of the model problem. The choice of our extrapolation parameter is flexible and includes the popular extrapolation parameter adopted in the restarted fast iterative shrinking-threshold algorithm (FISTA). By providing a unified analysis framework of descent methods, we establish the convergence of the full sequence under the assumption that a suitable merit function satisfies the Kurdyka–Łojasiewicz property. Our algorithm exhibits linear convergence for the scale-invariant sparse signal reconstruction problem and the Rayleigh quotient problem over spherical constraint. When the denominator is the maximum of finitely many continuously differentiable weakly convex functions, we also propose another extrapolated proximal subgradient algorithm with guaranteed convergence to a stronger notion of stationary points of the model problem. Finally, we illustrate the proposed methods by both analytical and simulated numerical examples.

A Differential Evolution Algorithm for Multi-objective Sparse Reconstruction

Aims: This paper proposes a differential evolution algorithm to solve the multi-objective sparse reconstruction problem (DEMOSR). Background: The traditional method is to introduce the regularization coefficient and solve this problem through a regularization framework. But in fact, the sparse reconstruction problem can be regarded as a multi-objective optimization problem about sparsity and measurement error (two contradictory objectives). Objective: A differential evolution algorithm to solve multi-objective sparse reconstruction problem (DEMOSR) in sparse signal reconstruction and the practical application. Methods: First of all, new individuals are generated through tournament selection mechanism and differential evolution. Secondly, the iterative half thresholding algorithm is used for local search to increase the sparsity of the solution. To increase the diversity of solutions, a polynomial mutation strategy is introduced. Results: In sparse signal reconstruction, the performance of DEMOSR is better than MOEA/D-ihalf and StEMO. In addition, it can verify the effectiveness of DEMOSR in practical applications for sparse reconstruction of magnetic resonance images. Conclusions: According to the experimental results of DEMOSR in sparse signal reconstruction and the practical application of reconstructing magnetic resonance images, it can be proved that DEMOSR is effective in sparse signal and image reconstruction.

Two-Dimensional ISAR Fusion Imaging of Block Structure Targets

The range resolution and azimuth resolution are restricted by the limited transmitting bandwidth and observation angle in a monostatic radar system. To improve the two-dimensional resolution of inverse synthetic aperture radar (ISAR) imaging, a fast linearized Bregman iteration for unconstrained block sparsity (FLBIUB) algorithm is proposed to achieve multiradar ISAR fusion imaging of block structure targets. First, the ISAR imaging echo data of block structure targets is established based on the geometrical theory of the diffraction model. The multiradar ISAR fusion imaging is transformed into a signal sparse representation problem by vectorization operation. Then, considering the block sparsity of the echo data of block structure targets, the FLBIUB algorithm is utilized to achieve the block sparse signal reconstruction and obtain the fusion image. The algorithm further accelerates the iterative convergence speed and improves the imaging efficiency by combining the weighted back-adding residual and condition number optimization of the basis matrix. Finally, simulation experiments show that the proposed method can effectively achieve block sparse signal reconstruction and two-dimensional multiradar ISAR fusion imaging of block structure targets.

Distributed Compressed Sensing Based Channel Parameter Estimation for MIMO-FBMC Communications

For the sparse correlation between channels in multiple input multiple output filter bank multicarrier with offset quadrature amplitude modulation (MIMO-FBMC/OQAM) systems, the distributed compressed sensing (DCS)-based channel estimation approach is studied. A sparse adaptive distributed sparse channel estimation method based on weak selection threshold is proposed. Firstly, the correlation between MIMO channels is utilized to represent a joint sparse model, and channel estimation is transformed into a joint sparse signal reconstruction problem. Then, the number of correlation atoms for inner product operation is optimized by weak selection threshold, and sparse signal reconstruction is realized by sparse adaptation. The experiment results show that proposed DCS-based method not only estimates the multipath channel components accurately but also achieves higher channel estimation performance than classical orthogonal matching pursuit (OMP) method and other traditional DCS methods in the time-frequency dual selective channels.