NDLI: A Predual Proximal Point Algorithm Solving a Non Negative Basis Pursuit Denoising Model

Content Provider	Springer Nature Link
Author	Malgouyres, F. Zeng, T.
Copyright Year	2009
Abstract	This paper develops an implementation of a Predual Proximal Point Algorithm (PPPA) solving a Non Negative Basis Pursuit Denoising model. The model imposes a constraint on the l $^{2}$ norm of the residual, instead of penalizing it. The PPPA solves the predual of the problem with a Proximal Point Algorithm (PPA). Moreover, the minimization that needs to be performed at each iteration of PPA is solved with a dual method. We can prove that these dual variables converge to a solution of the initial problem.Our analysis proves that we turn a constrained non differentiable convex problem into a short sequence of nice concave maximization problems. By nice, we mean that the functions which are maximized are differentiable and their gradient is Lipschitz.The algorithm is easy to implement, easier to tune and more general than the algorithms found in the literature. In particular, it can be applied to the Basis Pursuit Denoising (BPDN) and the Non Negative Basis Pursuit Denoising (NNBPDN) and it does not make any assumption on the dictionary. We prove its convergence to the set of solutions of the model and provide some convergence rates.Experiments on image approximation show that the performances of the PPPA are at the current state of the art for the BPDN.
Starting Page	294
Ending Page	311
Page Count	18
File Format	PDF
ISSN	09205691
Journal	International Journal of Computer Vision
Volume Number	83
Issue Number	3
e-ISSN	15731405
Language	English
Publisher	Springer US
Publisher Date	2009-03-14
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Basis Pursuit Algorithm Sparse representation Proximal point algorithm ell1 minimization Pattern Recognition Image Processing and Computer Vision Artificial Intelligence (incl. Robotics) Computer Imaging, Vision, Pattern Recognition and Graphics
Content Type	Text
Resource Type	Article
Subject	Artificial Intelligence Computer Vision and Pattern Recognition Software

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