  The recovery of the underlying low-rank structure of clean data corrupted
with sparse noise/outliers is attracting increasing interest. However, in many
low-level vision problems, the exact target rank of the underlying structure
and the particular locations and values of the sparse outliers are not known.
Thus, the conventional methods cannot separate the low-rank and sparse
components completely, especially in the case of gross outliers or deficient
observations. Therefore, in this study, we employ the minimum description
length (MDL) principle and atomic norm for low-rank matrix recovery to overcome
these limitations. First, we employ the atomic norm to find all the candidate
atoms of low-rank and sparse terms, and then we minimize the description length
of the model in order to select the appropriate atoms of low-rank and the
sparse matrices, respectively. Our experimental analyses show that the proposed
approach can obtain a higher success rate than the state-of-the-art methods,
even when the number of observations is limited or the corruption ratio is
high. Experimental results utilizing synthetic data and real sensing
applications (high dynamic range imaging, background modeling, removing noise
and shadows) demonstrate the effectiveness, robustness and efficiency of the
proposed method.
