A Robust Fully Correntropy–Based Sparse Modeling Alternative to Dictionary Learning

Correntropy is a dependence measure that goes beyond Gaussian environments and optimizations based on Minimum Squared Error (MSE). Its ability to induce a metric that is fully modulated by a single parameter makes it an attractive tool for adaptive signal processing. We propose a sparse modeling framework based on the dictionary learning technique known as K–SVD where Correntropy replaces MSE in the sparse coding and dictionary update subroutines. The former yields a robust variant of Orthogonal Matching Pursuit while the latter exploits robust Singular Value Decompositions. The result is Correntropy–based dictionary learning. The data–driven nature of the approach combines two appealing features in unsupervised learning—robustness and sparseness—without adding hyperparameters to the framework. Robust recovery of bases in synthetic data and image denoising under impulsive noise confirm the advantages of the proposed techniques.