Polyblur: Removing Mild Blur by Polynomial Reblurring

Delbracio, Mauricio; Garcia-Dorado, Ignacio; Choi, Sungjoon; Kelly, Damien P.; Milanfar, Peyman

doi:10.1109/tci.2021.3100998

Cited by 27 publications

(30 citation statements)

References 62 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…where the transfer function H is defined by (7). Assume that we deal with a linear convolution filter and H is fixed.…”

Section: Proposed Approachmentioning

confidence: 99%

“…In spite that the reverse image filtering idea was introduced very recently [30], it has already contributed to developing new deep learning architectures [6], studies on iterative depth B Alexander G. Belyaev a.belyaev@hw.ac.uk Lizhong Wang lw56@hw.ac.uk Pierre-Alain Fayolle fayolle@u-aizu.ac.jp 1 Heriot-Watt University, Edinburgh, UK 2 University of Aizu, Aizu-Wakamatsu, Japan and image super-resolution [22,35], and image restoration and sharpening [7,28].…”

Section: Introduction and Contributionsmentioning

confidence: 99%

See 1 more Smart Citation

Reverse image filtering with clean and noisy filters

Wang

Fayolle

Belyaev

2022

SIViP

View full text Add to dashboard Cite

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.

show abstract

“…where the transfer function H is defined by (7). Assume that we deal with a linear convolution filter and H is fixed.…”

Section: Proposed Approachmentioning

confidence: 99%

Section: Introduction and Contributionsmentioning

confidence: 99%

Reverse image filtering with clean and noisy filters

Wang

Fayolle

Belyaev

2022

SIViP

View full text Add to dashboard Cite

show abstract

“…Due to the assumptions and approximations, the R-method can only reverse the effects of filters which mildly alter the original image. In a recent paper [50], similar ideas as that of the R-and T-method are used to develop an algorithm to remove mild defocus and motion blur from natural images.…”

Section: Appendix Amentioning

confidence: 99%

Fast image reverse filters through fixed point and gradient descent acceleration

Galetto¹,

Deng²

2022

Preprint

View full text Add to dashboard Cite

In this paper, we study the problem of reverse image filtering. An image filter denoted g(.), which is available as a black box, produces an observation b = g(x) when provided with an input x. The problem is to estimate the original input signal x from the black box filter g(x) and the observation b. We study and re-develop state-of-the-art methods from two points of view, fixed point iteration and gradient descent. We also explore the application of acceleration techniques for the two types of iterations. Through extensive experiments and comparison, we show that acceleration methods for both fixed point iteration and gradient descent help to speed up the convergence of state-of-the-art methods.

show abstract

“…However, because of the assumptions and approximations, the R-method only performs well for filters which mildly alter the original image. In a recent paper [31], similar ideas as that of the R-and T-method are used to develop an algorithm to remove mild defocus and motion blur from natural images.…”

Section: Previous Workmentioning

confidence: 99%

Reverse image filtering using total derivative approximation and accelerated gradient descent

Galetto¹,

Deng²

2021

Preprint

View full text Add to dashboard Cite

In this paper, we address a new problem of reversing the effect of an image filter, which can be linear or nonlinear. The assumption is that the algorithm of the filter is unknown and the filter is available as a black box. We formulate this inverse problem as minimizing a local patch-based cost function and use total derivative to approximate the gradient which is used in gradient descent to solve the problem. We analyze factors affecting the convergence and quality of the output in the Fourier domain. We also study the application of accelerated gradient descent algorithms in three gradient-free reverse filters, including the one proposed in this paper. We present results from extensive experiments to evaluate the complexity and effectiveness of the proposed algorithm. Results demonstrate that the proposed algorithm outperforms the state-of-the-art in that (1) it is at the same level of complexity as that of the fastest reverse filter, but it can reverse a larger number of filters, and (2) it can reverse the same list of filters as that of the very complex reverse filter, but its complexity is much smaller.

show abstract

Polyblur: Removing Mild Blur by Polynomial Reblurring

Cited by 27 publications

References 62 publications

Reverse image filtering with clean and noisy filters

Reverse image filtering with clean and noisy filters

Fast image reverse filters through fixed point and gradient descent acceleration

Reverse image filtering using total derivative approximation and accelerated gradient descent

Contact Info

Product

Resources

About