0000000000362609
AUTHOR
Stanley Osher
showing 6 related works from this author
FAST EDGE-FILTERED IMAGE UPSAMPLING.
2011
We present a novel edge preserved interpolation scheme for fast upsampling of natural images. The proposed piecewise hyperbolic operator uses a slope-limiter function that conveniently lends itself to higher-order approximations and is responsible for restricting spatial oscillations arising due to the edges and sharp details in the image. As a consequence the upsampled image not only exhibits enhanced edges, and discontinuities across boundaries, but also preserves smoothly varying features in images. Experimental results show an improvement in the PSNR compared to typical cubic, and spline-based interpolation approaches.
A New Time Dependent Model Based on Level Set Motion for Nonlinear Deblurring and Noise Removal
1999
In this paper we summarize the main features of a new time dependent model to approximate the solution to the nonlinear total variation optimization problem for deblurring and noise removal introduced by Rudin, Osher and Fatemi. Our model is based on level set motion whose steady state is quickly reached by means of an explicit procedure based on an ENO Hamilton-Jacobi version of Roe's scheme. We show numerical evidence of the speed, resolution and stability of this simple explicit procedure in two representative 1D and 2D numerical examples.
A note on the Bregmanized Total Variation and dual forms
2009
This paper considers two approaches to perform image restoration while preserving the contrast. The first one is the Total Variation-based Bregman iterations while the second consists in the minimization of an energy that involves robust edge preserving regularization. We show that these two approaches can be derived form a common framework. This allows us to deduce new properties and to extend and generalize these two previous approaches.
Blind deconvolution using TV regularization and Bregman iteration
2005
In this paper we formulate a new time dependent model for blind deconvolution based on a constrained variational model that uses the sum of the total variation norms of the signal and the kernel as a regularizing functional. We incorporate mass conservation and the nonnegativity of the kernel and the signal as additional constraints. We apply the idea of Bregman iterative regularization, first used for image restoration by Osher and colleagues [S.J. Osher, M. Burger, D. Goldfarb, J.J. Xu, and W. Yin, An iterated regularization method for total variation based on image restoration, UCLA CAM Report, 04-13, (2004)]. to recover finer scales. We also present an analytical study of the model disc…
Explicit Algorithms for a New Time Dependent Model Based on Level Set Motion for Nonlinear Deblurring and Noise Removal
2000
In this paper we formulate a time dependent model to approximate the solution to the nonlinear total variation optimization problem for deblurring and noise removal introduced by Rudin and Osher [ Total variation based image restoration with free local constraints, in Proceedings IEEE Internat. Conf. Imag. Proc., IEEE Press, Piscataway, NJ, (1994), pp. 31--35] and Rudin, Osher, and Fatemi [ Phys. D, 60 (1992), pp. 259--268], respectively. Our model is based on level set motion whose steady state is quickly reached by means of an explicit procedure based on Roe's scheme [ J. Comput. Phys., 43 (1981), pp. 357--372], used in fluid dynamics. We show numerical evidence of the speed of resolution…
MRI resolution enhancement using total variation regularization
2009
We propose a novel method for resolution enhancement for volumetric images based on a variational-based reconstruction approach. The reconstruction problem is posed using a deconvolution model that seeks to minimize the total variation norm of the image. Additionally, we propose a new edge-preserving operator that emphasizes and even enhances edges during the up-sampling and decimation of the image. The edge enhanced reconstruction is shown to yield significant improvement in resolution, especially preserving important edges containing anatomical information. This method is demonstrated as an enhancement tool for low-resolution, anisotropic, 3D brain MRI images, as well as a pre-processing …