In this article we construct orthonormal bases for bi-variate
anisotropic α-modulation spaces. The construction is based on generating a
nice anisotropic α-covering and using carefully selected tensor products of
univariate brushlet functions with regards to this covering. As an application,
we show that n-term nonlinear approximation with the orthonormal bases in
certain anisotropic α-modulation spaces can be completely characterized.