Bayesian Learning for Low-Rank matrix reconstruction
This addresses matrix completion challenges in under-determined systems, though it appears incremental as it builds on existing Bayesian and low-rank methods.
The paper tackles the problem of reconstructing low-rank matrices from linear measurements without prior knowledge of rank or noise power, using Bayesian learning with latent variable models, and demonstrates reconstruction capabilities through numerical simulations.
We develop latent variable models for Bayesian learning based low-rank matrix completion and reconstruction from linear measurements. For under-determined systems, the developed methods are shown to reconstruct low-rank matrices when neither the rank nor the noise power is known a-priori. We derive relations between the latent variable models and several low-rank promoting penalty functions. The relations justify the use of Kronecker structured covariance matrices in a Gaussian based prior. In the methods, we use evidence approximation and expectation-maximization to learn the model parameters. The performance of the methods is evaluated through extensive numerical simulations.