Fast algorithms for image decomposition based on split Bregman technology

The image decomposition model based on total variation and homogeneous Besov spaces (TV-Besov) has gained great success in cartoon-texture decomposition. Since the TV norm is not differentiable, its numerical computation is very slow using PDEs based gradient descent methods. To overcome this difficulty, iterative descent algorithms were proposed based on split Bregman methods and fast Fourier transform(FFT) aiming for p = 1, p = 2 and p = ∞ respectively. Numerical simulations show that the proposed methods could effectively improve the convergence speed.