  We first propose the regular sketch-and-project method for solving tensor
equations with respect to the popular t-product. Then, three adaptive sampling
strategies and three corresponding adaptive sketch-and-project methods are
derived. We prove that all the proposed methods have linear convergence in
expectation. Furthermore, we investigate the Fourier domain versions and some
special cases of the new methods, where the latter corresponds to some famous
matrix equation methods. Finally, numerical experiments are presented to
demonstrate and test the feasibility and effectiveness of the proposed methods
for solving tensor equations
