A new variational model for removal of combined additive and multiplicative noise and a fast algorithm for its numerical approximation

作者：Chumchob Noppadol^*; Chen Ke; Brito Loeza Carlos

来源：International Journal of Computer Mathematics, 2013, 90(1): 140-161.

DOI：10.1080/00207160.2012.709625

• additive noise
• image denoising
• multiplicative noise
• nonlinear multigrid
• total variation
• variational models
• 68U10
• 65F22
• 65K10
• 65F10
• 65N55

Variational image restoration models for both additive and multiplicative noise (MN) removal are rarely encountered in the literature. This paper proposes a new variational model and a fast algorithm for its numerical approximation to remove independent additive and MN from digital images. Two previous works by L. Rudin, S. Osher, and E. Fatemi [Nonlinear total variation based noise removal algorithms, Phys. D 60 (1992), pp. 259268] and Z. Jin and X. Yang [Analysis of a new variational model for multiplicative noise removal, J. Math. Anal. Appl. 362 (2010), pp. 415426] are used to develop the new model. As a result, developing a fast numerical algorithm is difficult because the associated EulerLagrange equation is highly nonlinear and standard unilevel iterative methods are not appropriate. To this end, we develop an efficient nonlinear multigrid approach via a robust fixed-point smoother. Numerical tests using both synthetic and realistic images not only confirm that our new model delivers quality results but also that the proposed numerical algorithm allows a very fast numerical realization of the model.

• 出版日期2013-1-1