Conjugate Momentum Quadratic Penalty Alternating Minimization for Total Variation Image Restoration

Optimization algorithms are a key tool in image restoration. The Quadratic Penalty Alternating Minimization (QPAM) algorithm is an algorithm used to tackle image restoration challenges. However, the persistent challenge of slow convergence speed remains. Efforts have been made to enhance convergence speed, including extending the algorithm with Nesterov's momentum method. Yet, the algorithm displays oscillatory patterns during the minimization process, which may result in slow convergence speed. To address this issue, we proposed a conjugate gradient style momentum to accelerate the QPAM for image restoration. The iterative scheme of the proposed method consists of a proximal linearization that is re-formulated for the conjugate momentum acceleration. Experiments on both Gaussian and Poisson noise image restoration show that our proposed Conjugate Momentum QPAM is at par with or better than the original QPAM and its Nesterov-accelerated version in terms of CPU time.