CLEAR: Covariant LEAst-square Re-fitting with applications to image restoration

In this paper, we propose a new framework to remove parts of the systematic errors affecting popular restoration algorithms, with a special focus for image processing tasks. Generalizing ideas that emerged for $\ell_1$ regularization, we develop an approach re-fitting the results of standard methods towards the input data. Total variation regularizations and non-local means are special cases of interest. We identify important covariant information that should be preserved by the re-fitting method, and emphasize the importance of preserving the Jacobian (w.r.t. the observed signal) of the original estimator. Then, we provide an approach that has a "twicing" flavor and allows re-fitting the restored signal by adding back a local affine transformation of the residual term. We illustrate the benefits of our method on numerical simulations for image restoration tasks

Restoration of quadratically distorted images

The problem of the restoration of quadratically distorted images is considered in this investigation, based upon the fact that images formed by partially coherent illuminations are related quadratically to the amplitude of the object. Two of the most important problems in image restoration are: 1) determining the degradation characteristics of the degraded image and 2) developing restoration algorithms. Among the two classes of inverse problems, one for system identification and the second for image restoration, only the means to solve the latter are presented in this study. Since the present problem is represented by the second-order term of a Volterra series expansion, multidimensional Volterra filter theory is presented with emphasis on the properties of two-dimensional quadratic filter. The mathematics of inverse problems is presented for the purpose of image restoration, and the novel algorithms which are simple and easy to implement and robust to the ill-conditioned system in comparison to the existing algorithms are proposed. Since quadratically distorted imaging systems preclude a closed-form solution, approximate solutions are obtained through application of the proposed iterative and noniterative schemes. Images restored approximately by the proposed algorithms can be improved substantially by the use of a Newton-Raphson iteration scheme. Two typical regularization methods are presented and the truncated singular-value decomposition method is applied for the noisy image restoration. Regularized iterative restoration schemes for the noisy image restoration are also considered. Simulation examples for different issues are presented

Analysis of adversarial attacks against CNN-based image forgery detectors

With the ubiquitous diffusion of social networks, images are becoming a dominant and powerful communication channel. Not surprisingly, they are also increasingly subject to manipulations aimed at distorting information and spreading fake news. In recent years, the scientific community has devoted major efforts to contrast this menace, and many image forgery detectors have been proposed. Currently, due to the success of deep learning in many multimedia processing tasks, there is high interest towards CNN-based detectors, and early results are already very promising. Recent studies in computer vision, however, have shown CNNs to be highly vulnerable to adversarial attacks, small perturbations of the input data which drive the network towards erroneous classification. In this paper we analyze the vulnerability of CNN-based image forensics methods to adversarial attacks, considering several detectors and several types of attack, and testing performance on a wide range of common manipulations, both easily and hardly detectable

Convolutional Deblurring for Natural Imaging

In this paper, we propose a novel design of image deblurring in the form of one-shot convolution filtering that can directly convolve with naturally blurred images for restoration. The problem of optical blurring is a common disadvantage to many imaging applications that suffer from optical imperfections. Despite numerous deconvolution methods that blindly estimate blurring in either inclusive or exclusive forms, they are practically challenging due to high computational cost and low image reconstruction quality. Both conditions of high accuracy and high speed are prerequisites for high-throughput imaging platforms in digital archiving. In such platforms, deblurring is required after image acquisition before being stored, previewed, or processed for high-level interpretation. Therefore, on-the-fly correction of such images is important to avoid possible time delays, mitigate computational expenses, and increase image perception quality. We bridge this gap by synthesizing a deconvolution kernel as a linear combination of Finite Impulse Response (FIR) even-derivative filters that can be directly convolved with blurry input images to boost the frequency fall-off of the Point Spread Function (PSF) associated with the optical blur. We employ a Gaussian low-pass filter to decouple the image denoising problem for image edge deblurring. Furthermore, we propose a blind approach to estimate the PSF statistics for two Gaussian and Laplacian models that are common in many imaging pipelines. Thorough experiments are designed to test and validate the efficiency of the proposed method using 2054 naturally blurred images across six imaging applications and seven state-of-the-art deconvolution methods.Comment: 15 pages, for publication in IEEE Transaction Image Processin

Image blur estimation based on the average cone of ratio in the wavelet domain

In this paper, we propose a new algorithm for objective blur estimation using wavelet decomposition. The central idea of our method is to estimate blur as a function of the center of gravity of the average cone ratio (ACR) histogram. The key properties of ACR are twofold: it is powerful in estimating local edge regularity, and it is nearly insensitive to noise. We use these properties to estimate the blurriness of the image, irrespective of the level of noise. In particular, the center of gravity of the ACR histogram is a blur metric. The method is applicable both in case where the reference image is available and when there is no reference. The results demonstrate a consistent performance of the proposed metric for a wide class of natural images and in a wide range of out of focus blurriness. Moreover, the proposed method shows a remarkable insensitivity to noise compared to other wavelet domain methods