Matrix scale ambiguity correction with non-positive definite regularizers in blind inverse problems

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.