<p>Image restoration is a fundamental task in image processing, aiming to recover images from degraded observations. Inverse problems in image restoration are often ill-posed, requiring regularization techniques to obtain stable and meaningful solutions. Total Variation (TV) regularization has proven to be an effective approach for preserving image edges while suppressing noise. However, solving TV-based restoration problems efficiently remains a challenge due to their non-smooth and non-differentiable nature. To address this, operator splitting methods such as the Quadratic Penalty Alternating Minimization (QPAM) algorithm have been widely used. However, its convergence rate limits its practical applicability for large-scale image restoration. To accelerate the algorithm, we propose <b>Conjugate Momentum Quadratic Penalty Alternating Minimization (CG-QPAM)</b>, an enhanced optimization framework that integrates the conjugate momentum method into QPAM for a faster and more stable convergence. We provide a convergence analysis proving that CG-QPAM achieves an improved theoretical rate over QPAM. Our analysis establishes that the incorporation of CG momentum significantly enhances the stability and efficiency of the algorithm. Experimental results on TV image restoration demonstrate that CG-QPAM significantly accelerates the convergence compared to the original QPAM and other accelerated operator splitting methods, while maintaining competitive reconstruction quality. These findings suggest that CG-QPAM is a promising approach for accelerating TV-based image restoration and can be extended to other inverse problems in imaging science.</p>