Multichannel interpolation of nonuniform samples with application to image recovery

摘要

The multichannel trigonometric reconstruction from uniform samples was proposed recently. It not only makes use of multichannel information about the signal but is also capable to generate various kinds of interpolation formulas according to the types and amounts of the collected samples. The paper presents the theory of multichannel interpolation from nonuniform samples. Two distinct models of nonuniform sampling patterns are considered, namely recurrent and generic nonuniform sampling. Each model involves two types of samples: nonuniform samples of the observed signal and its derivatives. Numerical examples and quantitative error analysis are provided to demonstrate the effectiveness of the proposed algorithms. Additionally, the proposed algorithms for recovering highly corrupted images are also investigated. In comparison with the median filter and the Shepard interpolation, the proposed algorithms produce superior results with lower errors. (C) 2019 Elsevier B.V. All rights reserved.