MINIMIZING QUOTIENT REGULARIZATION MODEL

Quotient regularization models (QRMs) are a class of powerful reg-ularization techniques that have gained considerable attention in recent years, due to their ability to handle complex and highly nonlinear data sets. How-ever, the nonconvex nature of QRM poses a significant challenge in finding its optimal solution. We are interested in scenarios where both the numerator and the denominator of QRM are absolutely one-homogeneous functions, which is widely applicable in the fields of signal processing and image processing. In this paper, we utilize a gradient flow to minimize such QRM in combination with a quadratic data fidelity term. Our scheme involves solving a convex problem iteratively. The convergence analysis is conducted on a modified scheme in a continuous formulation, showing the convergence to a stationary point. Numerical experiments demonstrate the effectiveness of the proposed algorithm in terms of accuracy, outperforming the state-of-the-art QRM solvers.