We prove that a simple geometric theory of SU-rank 1 is n-ample if and only if the associated theory equipped with an predicate for an independent dense subset is n-ample for n at least 2.

We explore the size of the largest (permuted) triangular submatrix of a random matrix, and more precisely its asymptotical behavior as the size of the ambient matrix tends to infinity. The importance of such permuted triangular submatrices arises when dealing with certain combinatorial algebraic settings in which these submatrices determine the rank of the ambient matrix, and thus attract a spe...

In real applications, our observations are often noisy, or even grossly corrupted, and some observations may be missing. This fact naturally leads to the problem of recovering a low-rank matrix X from a corrupted observation matrix X = X + E (each column of X is an observation vector), with E being the unknown noise. Due to the low-rank property of X, it is straightforward to consider the follo...

Learning-based superresolution reconstruction is an efficient image processing technique that has become a popular topic in recent years. Since ill-conditioned problem, appropriate priors or examples are the key factors for recovering high-quality images with rich details. However, some current advanced methods, mappings established using dictionaries of low- and high-resolution cannot effectiv...