Blind inverse problems suffer from scale indeterminacy. The Alternated Minimization using the Optimal ReScaling (AMORS) method addresses this issue by integrating a scalar that compensates for the indeterminacy. Cohen and Leplat correct the indeterminacy by a diagonal matrix in tensor factorization but require positive definite regularizations. We propose to extend these works to matrix compensation without positive definiteness, allowing the use of total variation. We introduce a flexible tuning of the regularizations per column of the estimated matrices. We obtain stable and fast convergence when dealing with dictionary learning in the context of functional connectivity in fMRI.
Moudoud et al. (Thu,) studied this question.