2015/01/12 by Martin Sundin, Sundin, Martin, Saikat Chatterjee +3
Computer Science · Engineering · Mathematics · #Blind Source Separation Techniques #FOS: Computer and information sciences #Image and Signal Denoising Methods #Machine Learning (stat.ML) #Sparse and Compressive Sensing Techniques #stat.ML
paper · pdf · doi:10.48550/arxiv.1501.02579
Submitted to IEEE Transactions on Signal Processing
arxiv created 2015/01/12 · openalex publication_date 2015/01/12 · arxiv updated 2015/01/13 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
Using a Bayesian approach, we consider the problem of recovering sparse signals under additive sparse and dense noise. Typically, sparse noise models outliers, impulse bursts or data loss. To handle sparse noise, existing methods simultaneously estimate the sparse signal of interest and the sparse noise of no interest. For estimating the sparse signal, without the need of estimating the sparse noise, we construct a robust Relevance Vector Machine (RVM). In the RVM, sparse noise and ever present dense noise are treated through a combined noise model. The precision of combined noise is modeled by a diagonal matrix. We show that the new RVM update equations correspond to a non-symmetric sparsity inducing cost function. Further, the combined modeling is found to be computationally more efficient. We also extend the method to block-sparse signals and noise with known and unknown block structures. Through simulations, we show the performance and computation efficiency of the new RVM in several applications: recovery of sparse and block sparse signals, housing price prediction and image denoising.