# Nonlinear total variation based noise removal algorithms

##### Citations

40,257 citations

17,433 citations

### Cites background from "Nonlinear total variation based noi..."

...There is a vast literature, but some important modern papers are those on total variation denoising [145], soft thresholding [49], the lasso [156], basis pursuit [34], compressed sensing [50, 28, 29], and structure learning of sparse graphical models [123]....

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...This problem is often called total variation denoising [145], and has applications in signal processing....

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14,587 citations

10,404 citations

### Cites methods from "Nonlinear total variation based noi..."

...The algorithm is as follows (we essentially adopt the method from [23] for the discretization of the divergence operator and the iterative algorithm from [1]): knowing , we first compute and using (6) and (7), respectively....

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9,950 citations

### Cites methods from "Nonlinear total variation based noi..."

...Experiments with standard time-frequency dictionaries indicate some of the potential bene ts of BP. Experiments with some nonstandard dictionaries { like the stationary wavelet dictionary and the Heaviside dictionary { indicate important connections between BP and methods like Mallat and Zhong's Multi-Scale Edge Representation and Osher, Rudin and Fatemi's Total Variation-based De-Noising methods....

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...Recently, Rudin, Osher and Fatemi [31] have called attention to the possibility of de-noising images using total-variation penalized least-squares....

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##### References

13,020 citations

2,565 citations

### "Nonlinear total variation based noi..." refers background or methods in this paper

...Additionally, in [8], Alvarez, Lions and Morel devised an interesting stable image restoration algorithm based on mean curvature motion, see also ref....

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...[8] as a model for smoothing and edge detection....

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1,879 citations

### Additional excerpts

...The first attempt along these lines was made by Phillips [1] and later refined by Twomey [2] [3] in the one-dimensional case....

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1,205 citations

### "Nonlinear total variation based noi..." refers background in this paper

...We remark that Geman and Reynolds, in a very interesting paper [10] , proposed minimizing various nonlinear functionals of the form f q~(~x 2 + u 2) dx dy 12 with constraints....

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1,142 citations

### "Nonlinear total variation based noi..." refers methods in this paper

...The theoretical justification for this approach comes from the fact that it is merely the gradient-projection method of Rosen [14]....

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