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Highlights • A collaborative block compressed sensing (CBCS) framework is proposed where the local structure information and perceptual nonlocal similarity are considered to better characterize the structural details and maintain the smoothness of the pixels. • The combination of the syntheses and analysis sparse coding is applied in the formulated CBCS, which could better explore the sparsity of the signal. • An efficient iterative appraoch based on Multi-criteria Nash equilibrium techinique is proposed to solve the reconstruction problem, resulting in a better performance than the compared state-of-the-art BCS methods. Abstract In the past decade, image reconstruction based on compressed sensing (CS) has attracted great interest from researchers in signal processing. Due to the tremendous amount of information that an image contains, block compressed sensing (BCS) is often applied to divide an entire image into non-overlapping sub-blocks, treating all sub-blocks separately. However, an independent reconstruction ignores the correlation between adjacent sub-blocks and results in quality degradation, both in objective and subjective assessments. To obtain a satisfactory reconstructed image, this paper proposes a collaborative BCS (CBCS) framework with dual-domain sparse representation, where local structural information (LSI) and non-local pixel similarity are jointly considered. During a reconstruction, a local data-adaptive kernel regressor is introduced to extract the local image structure, which helps build a correlation of pixels between adjacent sub-blocks and preserves the details of an image. At the same time, a perceptually non-local similarity (PNLS), based on the human visual system, is used to improve visual quality. In addition, we employed both an analysis model and a synthesis model to further enhance sparseness and to formulate a dual-domain sparse representation based BCS reconstruction problem. Finally, an efficient, iterative approach, based on the multi-criteria Nash equilibrium technique, is proposed to solve this problem. Experimental results on benchmark images demonstrate that the proposed method can achieve competitive results both in both numerical and visual comparisons with some state-of-the-art BCS algorithms. [ABSTRACT FROM AUTHOR]

• Feature selection (FS) of high-dimensional data is reformulated as a many-objective optimization problem (MaOP) , consisting of three objectives to be minimized simultaneously. • To solve the formulated problem, we developed a PSO-based algorithm to search for the Pareto optimal solutions with two-level particle cooperation under the MOEA/D framework. • We made a systematical comparison between these the proposed methods and some state-of-the-art single objective and other MaOP FS approaches and the results demonstrate the efficacy of our proposed methods both in classification accuracy on the test data and the size of the feature subset. Feature selection (FS) plays a crucial role in classification, which aims to remove redundant and irrelevant data features.unknown However, for high-dimensional FS problems, Pareto optimal solutions are usually sparse, signifying that most of the decision variables are zero. Solving such problems using most existing evolutionary algorithms is difficult. In this paper, we reformulate FS as a many-objective optimization problem comprising three objectives to be minimized. To solve this problem, we proposed a binary particle swarm optimization with a two-level particle cooperation strategy. In the first level, to maintain rapid convergence, randomly generated ordinary particles and strict particles filtered by ReliefF are combined as the initialized particles. In the second level, under the decomposition multiobjective optimization framework, cooperation between particles is conducted during the update process to search for Pareto solutions more efficiently. In addition, a many-objective reset operation is proposed to enable the algorithm to jump out of the local optimum. Experimental studies on 10 real-world benchmark data sets revealed that our proposed algorithm could effectively reduce the number of features and achieve a competitive classification accuracy compared with some state-of-the-art evolutionary FS methods and non-evolutionary approaches. [ABSTRACT FROM AUTHOR]

Dictionary learning (DL) based block compressive sensing (BCS) aims to obtain both good sparse representation and reconstructed image with high precision. Traditional methods always combines these two objectives together into one single-level optimization problem by Lagrangian multiplier or optimize one objective by fixing the other one as a constraint, which makes the problem much easier to solve. However, when independent measurement noise exists, the recovered sub-block and the sparse coefficients are no longer simply bridged by linear function but have a more complex relationship with each other. In addition, the major task in BCS focuses on optimizing the recovered sub-block. To accurately address the intrinsically mutual influences between the two tasks and stress the importance of major task, DL based BCS is formulated as a bi-level optimization problem in which the upper level is to approximate the reconstructed sub-block by minimizing the CS measurement discrepancy and the lower level is to optimize the sparse coefficients represented by locally learned dictionary by minimizing the sparsity of the image sub-block. In this bilevel problem, the perceptual nonlocal similarity (PNLS) is proposed as the constraint for the upper-level optimization, which can reduce the block artifact among the sub-blocks. In order to solve this problem, a combination of l 1 and l 2 norm minimization method is used. Experimental results demonstrate that the proposed bilevel optimization method is effective and achieves higher performance on numerical and visual results than some state-of-the-art single-level optimization methods in BCS. [ABSTRACT FROM AUTHOR]