This paper describes the complete implementation of a blind image denoising algorithm, that takes any digital image as input. In a first step the algorithm estimates a Signal and Frequency Dependent (SFD) noise model. In a second step, the image is denoised by a multiscale adaptation of the Non-local Bayes denoising method. We focus here on a careful analysis of the denoising step and present a detailed discussion of the influence of its parameters. Extensive commented tests of the blind denoising algorithm are presented, on real JPEG images and on scans of old photographs. Source CodeThe source code (ANSI C), its documentation, and the online demo are accessible at the IPOL web page of this article 1 .

Digital images are matrices of equally spaced pixels, each containing a photon count. This photon count is a stochastic process due to the quantum nature of light. It follows that all images are noisy. Ever since digital images have existed, numerical methods have been proposed to improve the signal-to-noise ratio. Such ‘denoising’ methods require a noise model and an image model. It is relatively easy to obtain a noise model. As will be explained in the present paper, it is even possible to estimate it from a single noisy image.

Arguably several thousands papers are dedicated to image denoising. Most papers assume a fixed noise model, mainly white Gaussian or Poissonian. This assumption is only valid for raw images. Yet, in most images handled by the public and even by scientists, the noise model is imperfectly known or unknown. End users only dispose the result of a complex image processing chain effectuated by uncontrolled hardware and software (and sometimes by chemical means). For such images, recent progress in noise estimation permits to estimate from a single image a noise model, which is simultaneously signal and frequency dependent. We propose here a multiscale denoising algorithm adapted to this broad noise model. This leads to a blind denoising algorithm which we demonstrate on real JPEG images and on scans of old photographs for which the formation model is unknown. The consistency of this algorithm is also verified on simulated distorted images. This algorithm is finally compared with the unique state of the art previous blind denoising method.

The COVID-19 pandemic has undergone frequent and rapid changes in its local and global infection rates, driven by governmental measures or the emergence of new viral variants. The reproduction number Rt indicates the average number of cases generated by an infected person at time t and is a key indicator of the spread of an epidemic. A timely estimation of Rt is a crucial tool to enable governmental organizations to adapt quickly to these changes and assess the consequences of their policies. The EpiEstim method is the most widely accepted method for estimating Rt. But it estimates Rt with a significant temporal delay. Here, we propose a method, EpiInvert, that shows good agreement with EpiEstim, but that provides estimates of Rt several days in advance. We show that Rt can be estimated by inverting the renewal equation linking Rt with the observed incidence curve of new cases, it. Our signal-processing approach to this problem yields both Rt and a restored it corrected for the “weekend effect” by applying a deconvolution and denoising procedure. The implementations of the EpiInvert and EpiEstim methods are fully open source and can be run in real time on every country in the world and every US state.

In the article An Automatic Approach to Lossy Compression of AVIRIS Images N.N. Ponomarenko et al. propose a new method to specifically compress AVIRIS (Airborne Visible/Infrared Imaging Spectrometer) images. As part of the compression algorithm, a noise estimation is performed with a proposed new algorithm based on the computation of the variance of overlapping 8 × 8 blocks. The noise is estimated on the high-frequency orthonormal DCT-II coefficients of the blocks. To avoid the effect of edges and textures, the blocks are sorted according to their energy measured on a set of low-frequency coefficients. The final noise estimation is obtained by computing the median of the variances measured on the high-frequency part of the spectrum of the blocks using only those whose energy (measured on the low-frequencies) is low. A small percentile of the total set of blocks (typically the 0.5%) is used to select those blocks with the lower energy at the low-frequencies. Although the method measures uniform Gaussian noise, it can be easily adapted to deal with signal-dependent noise, which is realistic with the Poisson noise model obtained by a CCD device in a digital camera. Source CodeThe C++ implementation of the Ponomarenko et al. noise estimator version 3.0 is the one which has been peer reviewed and accepted by IPOL. The source code, the code documentation, and the online demo are available in the IPOL web page of this article 1 .

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Optimal denoising works at best on raw images (the image formed at the output of the focal plane, at the CCD or CMOS detector), which display a white signal-dependent noise. The noise model of the raw image is characterized by a function that given the intensity of a pixel in the noisy image returns the corresponding standard deviation; the plot of this function is the noise curve. This paper develops a nonparametric approach estimating the noise curve directly from a single raw image. An extensive cross-validation procedure is described to compare this new method with state-of-the-art parametric methods and with laboratory calibration methods giving a reliable ground truth, even for nonlinear detectors.

We propose a variational model for computing the effective reproduction number (ERN) of SARS-CoV-2 from the daily count of incident cases. This computation only requires the knowledge of the serial interval. The ERN estimate is made through the minimization of a functional that includes: (i) the adjustment of the incidence curve using an epidemiological model, (ii) the regularity of the estimation of the ERN and, (iii) the adjustment of the initial value to an initial estimate of R_0 obtained from the initial exponential growth of the epidemic. The model does not assume any statistical distribution for the ERN and, more importantly, does not require truncating the serial interval when its distribution contains negative days. A comparative study has been carried out with the standard EpiEstim method. For a particular choice of the parameters of the variational model and of the serial interval, a good agreement has been obtained between the estimate provided by the variational model and a 7 days shifted estimate obtained by EpiEstim. This backward shift suggests that our estimate is closer to present than that of EpiEstim. We also examine how to forecast the value of the ERN and the number of infected in the short term by two different extrapolation techniques. An implementation of the model is available online at www.ipol.im/ern.