Reverse image filtering using total derivative approximation and accelerated gradient descent

• URL: http://arxiv.org/abs/2112.04121v2
• Date: Thu, 9 Dec 2021 23:58:51 GMT
• Title: Reverse image filtering using total derivative approximation and accelerated gradient descent
• Authors: Fernando J. Galetto, Guang Deng
• Abstract summary: 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.
• Score: 82.93345261434943
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

Related papers

• Computational Doob's h-transforms for Online Filtering of Discretely Observed Diffusions [65.74069050283998]
  We propose a computational framework to approximate Doob's $h$-transforms. The proposed approach can be orders of magnitude more efficient than state-of-the-art particle filters.
  arXiv  Detail & Related papers  (2022-06-07T15:03:05Z)
• Learning Versatile Convolution Filters for Efficient Visual Recognition [125.34595948003745]
  This paper introduces versatile filters to construct efficient convolutional neural networks. We conduct theoretical analysis on network complexity and an efficient convolution scheme is introduced. Experimental results on benchmark datasets and neural networks demonstrate that our versatile filters are able to achieve comparable accuracy as that of original filters.
  arXiv  Detail & Related papers  (2021-09-20T06:07:14Z)
• Fourier Series Expansion Based Filter Parametrization for Equivariant Convolutions [73.33133942934018]
  2D filter parametrization technique plays an important role when designing equivariant convolutions. New equivariant convolution method based on the proposed filter parametrization method, named F-Conv. F-Conv evidently outperforms previous filter parametrization based method in image super-resolution task.
  arXiv  Detail & Related papers  (2021-07-30T10:01:52Z)
• Differentiable Particle Filtering without Modifying the Forward Pass [21.430102374292666]
  We show how to obtain unbiased estimators of the gradient of the marginal likelihood by only modifying messages used in backpropagation. We call it stop-gradient resampling, since it can easily be implemented with automatic differentiation libraries.
  arXiv  Detail & Related papers  (2021-06-18T18:58:52Z)
• Dilated filters for edge detection algorithms [0.0]
  Dilated convolution have impressive results in machine learning. We discuss here the idea of dilating the standard filters which are used in edge detection algorithms.
  arXiv  Detail & Related papers  (2021-06-14T12:52:17Z)
• Unsharp Mask Guided Filtering [53.14430987860308]
  The goal of this paper is guided image filtering, which emphasizes the importance of structure transfer during filtering. We propose a new and simplified formulation of the guided filter inspired by unsharp masking. Our formulation enjoys a filtering prior to a low-pass filter and enables explicit structure transfer by estimating a single coefficient.
  arXiv  Detail & Related papers  (2021-06-02T19:15:34Z)
• Stochastic Gradient Variance Reduction by Solving a Filtering Problem [0.951828574518325]
  Deep neural networks (DNN) are typically using optimized gradient descent (SGD) The estimation of the gradient using samples tends to be noisy and unreliable, resulting in large gradient variance and bad convergence. We propose textbfFilter Gradient Decent(FGD), an efficient optimization algorithm that makes the consistent estimation of gradient.
  arXiv  Detail & Related papers  (2020-12-22T23:48:42Z)
• Accelerated FBP for computed tomography image reconstruction [1.0266928164137636]
  Filtered back projection (FBP) is a commonly used technique in tomographic image reconstruction demonstrating acceptable quality. We propose a novel approach that reduces the computational complexity of the algorithm to $Theta(N2log N)$ addition operations avoiding Fourier space.
  arXiv  Detail & Related papers  (2020-07-13T10:16:54Z)
• Efficient Spatially Adaptive Convolution and Correlation [11.167305713900074]
  We provide a representation-theoretic framework that allows for spatially varying linear transformations to be applied to the filter. This framework allows for efficient implementation of extended convolution and correlation for transformation groups such as rotation (in 2D and 3D) and scale. We present applications to pattern matching, image feature description, vector field visualization, and adaptive image filtering.
  arXiv  Detail & Related papers  (2020-06-23T17:41:10Z)
• Filter Grafting for Deep Neural Networks: Reason, Method, and Cultivation [86.91324735966766]
  Filter is the key component in modern convolutional neural networks (CNNs) In this paper, we introduce filter grafting (textbfMethod) to achieve this goal. We develop a novel criterion to measure the information of filters and an adaptive weighting strategy to balance the grafted information among networks.
  arXiv  Detail & Related papers  (2020-04-26T08:36:26Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.