Iterative first-order reverse image filtering

We consider the problem of recovering an original image $${\varvec{x}}$$ x from its filtered version $${\varvec{y}}={\varvec{f}}({\varvec{x}})$$ y = f ( x ) , assuming that the internal structure of the filter $${\varvec{f}}(\cdot )$$ f ( · ) is unknown to us (i.e., we can only query the filter as a black-box and, for example, cannot invert it). We present two new iterative methods to attack the problem, analyze, and evaluate them on various smoothing and edge-preserving image filters.

Section: Numerical Experiments and Discussionmentioning

confidence: 99%

Section: Numerical Experiments and Discussionmentioning

confidence: 99%

“…(4). e Image-guided filtering using a smoothed guidance and defiltering with (4). See the main text for details.…”

Section: Numerical Experiments and Discussionmentioning

confidence: 99%

Section: Numerical Experiments and Discussionmentioning

confidence: 99%

Section: Introduction and Contributionmentioning

confidence: 99%

See 3 more Smart Citations

Two iterative methods for reverse image filtering

Belyaev

Fayolle

2021

Reverse image filtering with clean and noisy filters

Wang

Fayolle

Belyaev

2022

Given an image filter $${{\varvec{y}}}={{\varvec{f}}}\,({{\varvec{x}}})$$ y = f ( x ) , where $${{\varvec{x}}}$$ x and $${{\varvec{y}}}$$ y are input and output images, respectively, reverse image filtering consists of rendering an approximation to $${{\varvec{x}}}$$ x from $${{\varvec{y}}}$$ y using the filter $${{\varvec{f}}}\,(\cdot )$$ f ( · ) itself as a black box, without knowing the internal structure of the filter. In this paper, we propose to use modified Landweber iterations for reverse image filtering, evaluate the performance of our approach, and present applications to image deblurring and super-resolution. An important advantage of our approach over the existing reverse image filtering methods is high robustness to noise.

Fast iterative reverse filters using fixed-point acceleration

Deng

Galetto

2023

Iterative reverse filters have been recently developed to address the problem of removing effects of a black box image filter. Because numerous iterations are usually required to achieve the desired result, the processing speed is slow. In this paper, we propose to use fixed-point acceleration techniques to tackle this problem. We present an interpretation of existing reverse filters as fixed-point iterations and discuss their relationship with gradient descent. We then present extensive experimental results to demonstrate the performance of fixed-point acceleration techniques named after: Anderson, Chebyshev, Irons, and Wynn. We also compare the performance of these techniques with that of gradient descent acceleration. Key findings of this work include: (1) Anderson acceleration can make a non-convergent reverse filter convergent, (2) the T-method with an acceleration technique is highly efficient and effective, and (3) in terms of processing speed, all reverse filters can benefit from one of the acceleration techniques.