Poisson noise and Gaussian noise separation through copula theory

This study explores an innovative optimization problem in copula denoising, aiming to distinguish and eliminate both Poisson noise and Gaussian noise. Our solution encompasses two fundamental steps. First, it employs a modified guided Total Variation (BTV) regularization method to effectively suppress Gaussian noise. Then, it implements a Hellinger distance copula separation procedure to separate the Poisson noise from the pristine image. This dual-step approach ensures that crucial image features are preserved while significantly reducing noise levels. The paper includes analytical findings related to approximating the Poisson noise component and successfully resolving the proposed optimization model within a well-defined framework. To tackle the challenge of BTV minimization, an efficient projected Alternating Direction Method of Multipliers (ADMM) algorithm is introduced. The approach’s performance is demonstrated through comprehensive numerical experiments, illustrating noise reduction while maintaining essential image details and features. Comparative analyses further underscore the effectiveness of the proposed method.