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A Preference-Based Multiobjective Evolutionary Approach for Sparse Optimization.

Hui Li, Qingfu Zhang, Jingda Deng

    IEEE Transactions on Neural Networks and Learning Systems
    |April 4, 2017
    PubMed
    Summary
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    This study introduces a novel evolutionary approach for sparse optimization, effectively detecting true sparsity without prior estimation. The method enhances existing iterative thresholding techniques for improved signal reconstruction.

    Area of Science:

    • Signal Processing
    • Optimization
    • Machine Learning

    Background:

    • Iterative thresholding methods are widely used for sparse optimization problems, aiming to find a k-sparse solution.
    • A significant challenge in these methods is setting regularization parameters and estimating the true sparsity (k).

    Purpose of the Study:

    • To propose a preference-based multiobjective evolutionary approach to address shortcomings in iterative thresholding for sparse optimization.
    • To develop a method capable of detecting true sparsity and improving reconstruction in compressive sensing.

    Main Methods:

    • A preference-based multiobjective evolutionary algorithm is employed to search the knee region of the Pareto front.
    • The approach integrates iterative thresholding methods as local optimizers, eliminating the need for prior sparsity estimation.

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  • The method is designed to be extensible to sparse optimization problems with noise.

    • Main Results:

    • The proposed method effectively detects the true sparsity in noiseless scenarios by analyzing solution distributions.
    • Experimental results demonstrate the method's effectiveness in sparsity detection and enhancing reconstruction capabilities.
    • Performance was evaluated on artificial and magnetic resonance imaging (MRI) signals.

    Conclusions:

    • The developed preference-based multiobjective evolutionary approach offers a robust solution for sparse optimization problems.
    • This method overcomes limitations of traditional iterative thresholding by enabling automatic sparsity detection and improving signal reconstruction.
    • The approach shows significant promise for applications in compressive sensing and signal processing.