Resumen de Image decomposition using a second-order variational model and wavelet shrinkage
Minh-Phuong Tran, Thanh Nhan Nguyen
The paper is devoted to the new model for image decomposition, that splits an image f into three components u+v+w, where u a piecewise-smooth or the "cartoon" component, v a texture component and w the noise part in variational approach. This decomposition model in fact incorporates the advantages of two preceding models: the second-order total variation minimization of Rudin-Osher-Fatemi (ROF2), and wavelet shrinkage for oscillatory functions. This decomposition model is presented as an extension of the three components decomposition algorithm of Aujol et al. in [Dual norms and image decomposition models, Int. J. Comput. Vis. 63(1)(2005) 85–104]. It also continues the idea introduced previously by authors in [Denoising 3D medical images using a second order variational model and wavelet shrinkage, Imag. Anal. and Rec., Lecture Notes in Computer Science, 7325(2012), 138-145], for two components decomposition model. The ROF2 model was first proposed by Bergounioux et al. in [A second-order model for image denoising, Set-Valued Anal. and Var. Anal., 18(2010), 277-306], it is an improved regularization method to overcome the undesirable staircasing effect. The wavelet shrinkage is well combined to separate the oscillating part due to texture from that due to noise. Experimental results validate the proposed algorithm and demonstrate that the image decomposition model presents effective and comparable performance to other previous models.
