  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 algorithm
for recovering highly corrupted images is also investigated. In comparison with
the median filter and correction operation treatment, our approach produces
superior results with lower errors.
