Sequential Learning of Analysis Operators

In this paper two sequential algorithms for learning analysis operators are presented. They are built upon the same optimisation principle underlying both Analysis K-SVD and Analysis SimCO and use a stochastic gradient descent approach similar to ASimCO. The sequential analysis operator learning (SAOL) algorithm is based on projected gradient descent with an appropriately chosen step size while the implicit SAOL (ISAOL) algorithm avoids choosing a step size altogether by using a strategy inspired by the implicit Euler scheme for solving ordinary differential equations. Both algorithms are tested on synthetic and image data in comparison to Analysis SimCO and found to give slightly better recovery rates resp. decay of the objective function. In a final denoising experiment the presented algorithms are again shown to perform well in comparison to the state of the art algorithm ASimCO.