<p>In this paper, we propose a new variational model that utilizes the second fundamental form as the regularizer for the task of multiplicative noise removal. By leveraging the geometric properties of the proposed regularizer, the model exhibits improved preservation of geometric features, particularly for inclined planes. Theoretical analysis is also conducted to illustrate the advantages of the proposed regularizer in terms of contrast and corner preservations. However, we illustrate that the high-order nonlinearity and non-convexity of the proposed model make the explicit numerical scheme computationally expensive due to limited time step size. To address this, we employ the idea of scalar auxiliary variable (SAV) algorithm, which converts nonlinear terms into a scalar auxiliary variable, thereby transforming a nonlinear problem into a linear one that allows for larger time steps. Additionally, we apply the modified exponential SAV algorithm to an alternative scheme to obtain more accurate results. Importantly, these new schemes are theoretically proven to be unconditionally energy stable, and their detailed implementations are discussed to emphasize the suitability of the SAV-based algorithms. Extensive numerical experiments validate the superior performance of the proposed model and demonstrates the efficiency and stability of the proposed numerical schemes compared to other accelerated algorithms.</p>