An Efficient Coupled Dictionary Learning Method

Matlab code for the CDL method in 2019 paper "An Efficient Coupled Dictionary Learning Method"

A computationally efficient algorithm for learning a pair of coupled dictionaries {D1,D2} corresponding to the correlated joint dataset {X1, X2} so that D1A = X1 and D2A = X2. where A is the common sparse represenation matrix

Optimization problem:

{D1, D2} = argmin_{D1,D2,A} omega*||D1A-X1||_F^2 + (1-omega)||D2*A-X2||_F^2

           s.t. ||A_i||_0 < k , i, 1,...,N and
           
               ||D1_t||_2 = 1 ,||D2_t||_2 = 1 , t = 1,...,K

Input variables:

opts.omega: tuning parameter (default: 0.5)

opts.K: number of atoms in dictionaries (default: 4*max([size(X1,1),size(X1,1)]))

opts.k: maximum number of nonzero entries in columns of A (default: max([size(X1,1),size(X1,1)])/4)

opts.Nit: number of CDL iterations (default: 10)

opts.eps: approximation accuracy threshold (default: 1e-4)

opts.D1 and opts.D1: initial dictionaries (default: DCT dictionaries)

opts.DCatom ('true' or 'false') if true, keeps DC atom unchanged (default: true)

Refrence: F. G. Veshki and S. A. Vorobyov, "An Efficient Coupled Dictionary Learning Method," in IEEE Signal Processing Letters, vol. 26, no. 10, pp. 1441-1445, Oct. 2019, doi: 10.1109/LSP.2019.2934045.

(the mexOMP algorithm used for sparse approximation is taken from SPAMS toolbox (see mexOMP.m file))