  Matrix completion constantly receives tremendous attention from many research
fields. It is commonly applied for recommender systems such as movie ratings,
computer vision such as image reconstruction or completion, multi-task learning
such as collaboratively modeling time-series trends of multiple sensors, and
many other applications. Matrix completion techniques are usually
computationally exhaustive and/or fail to capture the heterogeneity in the
data. For example, images usually contain a heterogeneous set of objects, and
thus it is a challenging task to reconstruct images with high levels of missing
data. In this paper, we propose the sparse reverse of principal component
analysis for matrix completion. The proposed approach maintains smoothness
across the matrix, produces accurate estimates of the missing data, converges
iteratively, and it is computationally tractable with a controllable upper
bound on the number of iterations until convergence. The accuracy of the
proposed technique is validated on natural images, movie ratings, and
multisensor data. It is also compared with common benchmark methods used for
matrix completion.
