Miguel Colom

Secrets of image denoising cuisine

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.

Multiscale Image Blind Denoising

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 Noise Clinic: a Blind Image Denoising Algorithm

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 Code The source code (ANSI C), its documentation, and the online demo are accessible at the IPOL web page of this article1.

Nonparametric noise estimation method for raw images

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.

A non-parametric approach for the estimation of intensity-frequency dependent noise

We present a non-parametric method estimating an intensity and frequency dependent noise from a single image. The noise model is estimated on image patches and can be used consequently in all patch-based denoising methods. The method applies to cases where no access is granted to the image noise model, in particular to scanned photographs and JPEG images. The general noise model and the method to evaluate it are validated by comparing the estimations with the corresponding ground-truth curves for raw and JPEG images. Denoising experiments on scanned photographs also support the efficiency of the estimation method.

Analysis and Extension of the Percentile Method, Estimating a Noise Curve from a Single Image

Given a white Gaussian noise signal Non a sampling grid, its variance � 2 can be estimated from a small w × w pixels sample. However, in natural images we observe ˜ U = U + N�, the combination of the geometry of the scene that is photographed and the added noise. In this case, estimating directly the standard deviation of the noise from w × w samples of ˜ U is not reliable since the measured standard deviation is not explained just by the noise but also by the geometry of U. The Percentile method tries to estimate the standard deviationfrom w × w blocks of a high-passed version of ˜ U by a small p-percentile of these standard deviations. The idea behind is that edges and textures in a block of the image increase the observed standard deviation but they never make it decrease. Therefore, a small percentile (0.5%, for example) in the list of standard deviations of the blocks is less likely to be affected by the edges and textures than a higher percentile (50%, for example). The 0.5%-percentile is empirically proven to be adequate for most natural, medical and microscopy images. The Percentile method is adapted to deal with signal-dependent noise, which is realistic with the Poisson noise model obtained by a CCD device in a digital camera.

The noise clinic: A universal blind denoising algorithm

Most papers on denoising methods assume a white Gaussian noise model. Yet in most images handled by the public or by scientific users, the noise model is unknown and is not white, because of the various processes applied to the image before it reaches the user: scanning, demosaicing, compression, de-convolution, etc. To cope with this wide ranging problem, we propose a blind multiscale denoising algorithm working for noise which is simultaneously signal and frequency dependent. On noisy images coming from diverse sources (JPEG, scans of old photographs, ...) we show perceptually convincing results. This algorithm is compared to the state-of-the-art and it is also validated on images with white noise.

Nonparametric Multiscale Blind Estimation of Intensity-Frequency-Dependent Noise

The camera calibration parameters and the image processing chain which generated a given image are generally not available to the receiver. This happens for example with scanned photographs and for most JPEG images. These images have undergone various nonlinear contrast changes and also linear and nonlinear filters. To deal with remnant noise in such images, we introduce a general nonparametric intensity and frequency-dependent noise model. We demonstrate by simulated and experiments with real images that this model, which requires the estimation of more than 1000 parameters, performs an efficient noise estimation. The proposed noise model is a patch model. Its estimation can therefore be used as a preliminary step to any patch-based denoising method. Our noise estimation method introduces several new tools for performing this complex estimation. One of them is a new sparse patch distance function permitting to find noisy patches with similar underlying geometry. A validation of the noise model and of its estimation method is obtained by comparing its results to ground-truth noise curves for both raw and JPEG-encoded images, and by visual inspection of the denoising results of real images. A fair comparison with the state of the art is also performed.

Analysis and Extension of the Ponomarenko et al. Method, Estimating a Noise Curve from a Single Image

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 Code The 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 article1.

IPOL: A new journal for fully reproducible research; analysis of four years development

After four years of development of the Image Processing On Line journal (IPOL), this article presents a first analysis and overview of its scientific and technical development. The main issues met and overcome from the beginning of the journal are described with a focus on the purpose of the journal to establish a state of the art on the main Image Processing topics. The evolution of the online demonstration is also presented with a first analysis of author/publisher criticism, which led to a proposal for a new modular architecture of its demo system.