- Sparse coding. Given the observed data
, sparse coding aims at solving the optimization problem:

where and denote the and norms of an input vector, respectively. is the number of non-zero coefficients. is the learned dictionary and is the sparse representation of . - Dictionary updating.
For the obtained
, update
such that

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

where denotes the Frobenius norm of an input matrix.

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.

2020-04-03