The multidimensional seismic data is first reformulated into patch form . Each column vector in is extracted from the multidimensional seismic data matrix. An example is given in Yu et al. (2015) and Chen et al. (2016a). Equations 1 and 2 then become
Problem 3 is a NP-hard problem, and directly finding the truly optimal is impossible and is usually solved by an approximation pursuit method, such as the orthogonal matching pursuit (OMP) algorithm. To solve problem 4 for the adaptive dictionary , there are several different algorithms.