Convergence acceleration for multiobjective sparse reconstruction via knowledge transfer

© Springer Nature Switzerland AG 2019. Multiobjective sparse reconstruction (MOSR) methods can potentially obtain superior reconstruction performance. However, they suffer from high computational cost, especially in high-dimensional reconstruction. Furthermore, they are generally implemented independently without reusing prior knowledge from past experiences, leading to unnecessary computational consumption due to the re-exploration of similar search spaces. To address these problems, we propose a sparse-constraint knowledge transfer operator to accelerate the convergence of MOSR solvers by reusing the knowledge from past problem-solving experiences. Firstly, we introduce the deep nonlinear feature coding method to extract the feature mapping between the search of the current problem and a previously solved MOSR problem. Through this mapping, we learn a set of knowledge-induced solutions which contain the search experience of the past problem. Thereafter, we develop and apply a sparse-constraint strategy to refine these learned solutions to guarantee their sparse characteristics. Finally, we inject the refined solutions into the iteration of the current problem to facilitate the convergence. To validate the efficiency of the proposed operator, comprehensive studies on extensive simulated signal reconstruction are conducted

Gridless Evolutionary Approach for Line Spectral Estimation with Unknown Model Order

Gridless methods show great superiority in line spectral estimation. These methods need to solve an atomic $l_0$ norm (i.e., the continuous analog of $l_0$ norm) minimization problem to estimate frequencies and model order. Since this problem is NP-hard to compute, relaxations of atomic $l_0$ norm, such as nuclear norm and reweighted atomic norm, have been employed for promoting sparsity. However, the relaxations give rise to a resolution limit, subsequently leading to biased model order and convergence error. To overcome the above shortcomings of relaxation, we propose a novel idea of simultaneously estimating the frequencies and model order by means of the atomic $l_0$ norm. To accomplish this idea, we build a multiobjective optimization model. The measurment error and the atomic $l_0$ norm are taken as the two optimization objectives. The proposed model directly exploits the model order via the atomic $l_0$ norm, thus breaking the resolution limit. We further design a variable-length evolutionary algorithm to solve the proposed model, which includes two innovations. One is a variable-length coding and search strategy. It flexibly codes and interactively searches diverse solutions with different model orders. These solutions act as steppingstones that help fully exploring the variable and open-ended frequency search space and provide extensive potentials towards the optima. Another innovation is a model order pruning mechanism, which heuristically prunes less contributive frequencies within the solutions, thus significantly enhancing convergence and diversity. Simulation results confirm the superiority of our approach in both frequency estimation and model order selection.Comment: This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessibl