access icon free Graph regularised sparse NMF factorisation for imagery de-noising

© The Institution of Engineering and Technology
Received 25/05/2017, Accepted 20/12/2017, Revised 14/12/2017, Published 22/12/2017

When utilising non-negative matrix factorisation (NMF) to decompose a data matrix into the product of two low-rank matrices with non-negative entries, the noisy components of data may be introduced into the matrix. Many approaches have been proposed to address the problem. Different from them, the authors consider the group sparsity and the geometric structure of data by introducing -norm and local structure preserving regularisation in the formulated objective function. A graph regularised sparse NMF de-noising approach is proposed to learn discriminative representations for the original data. Since the non-differentiability of -norm increases the computational cost, they propose an effective iterative multiplicative update algorithm to solve the objective function by using the Frobenius-norm of transpose coefficient matrix. Experimental results on facial image datasets demonstrate the superiority of the proposed approach over several state-of-the-art approaches.

Inspec keywords: iterative methods; sparse matrices; matrix decomposition; image denoising; image representation; graph theory; face recognition; learning (artificial intelligence)

Other keywords: transpose coefficient matrix. Frobenius-norm; nonnegative matrix factorisation; graph regularised sparse NMF factorisation; facial image datasets; iterative multiplicative update algorithm; ℓ2,1-norm; discriminative representation; two low-rank matrices product; graph regularised sparse NMF denoising approach; data matrix decomposition; local structure preserving regularisation; group sparsity; imagery denoising

Subjects: Interpolation and function approximation (numerical analysis); Computer vision and image processing techniques; Linear algebra (numerical analysis); Combinatorial mathematics; Combinatorial mathematics; Knowledge engineering techniques; Linear algebra (numerical analysis); Image recognition; Interpolation and function approximation (numerical analysis)

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