Mykhail L. Uss

Image informative maps for component- wise estimating parameters of signal- dependent noise

Abstract. We deal with the problem of blind parameter estimation of signal-dependent noise from mono-component image data. Multispectral or color images can be processed in a component-wise manner. The main results obtained rest on the assumption that the image texture and noise parameters estimation problems are interdependent. A two-dimensional fractal Brownian motion (fBm) model is used for locally describing image texture. A polynomial model is assumed for the purpose of describing the signal-dependent noise variance dependence on image intensity. Using the maximum likelihood approach, estimates of both fBm-model and noise parameters are obtained. It is demonstrated that Fisher information (FI) on noise parameters contained in an image is distributed nonuniformly over intensity coordinates (an image intensity range). It is also shown how to find the most informative intensities and the corresponding image areas for a given noisy image. The proposed estimator benefits from these detected areas to improve the estimation accuracy of signal-dependent noise parameters. Finally, the potential estimation accuracy (Cramér-Rao Lower Bound, or CRLB) of noise parameters is derived, providing confidence intervals of these estimates for a given image. In the experiment, the proposed and existing state-of-the-art noise variance estimators are compared for a large image database using CRLB-based statistical efficiency criteria.

Maximum likelihood estimation of spatially correlated signal-dependent noise in hyperspectral images

Abstract. A new algorithm is described for estimating the noise model parameters in hyperspectral data when neither noise components variance nor noise spatial/spectral correlation priors are available. A maximum likelihood (ML) technique is introduced for checking the noise spatial correlation hypothesis and estimating the spatial correlation function width alongside with estimating signal-independent and signal-dependent noise components variance. The hyperspectral image is assumed to match a limited set of assumptions. A three-dimensional (3-D) fractional Brownian motion (fBm) model is introduced for describing locally the texture of the 3-D image noisy textural fragment. Nonstationarity of the useful image signal is taken into account by performing the estimation locally on a 3-D block-by-block basis. The accuracy of the proposed algorithm is first illustrated for synthetic images obtained from either pure fBm or almost noise-free AVIRIS hyperspectral images artificially degraded with spatially correlated noise. The results obtained for synthetic images demonstrate appropriate accuracy and robustness of the proposed method. Then results obtained for real life AVIRIS hyperspectral data sets confirm the noise spatial uncorrelation hypothesis for images acquired by the AVIRIS sensor. Conclusions and open problems are outlined.

VST-based lossy compression of hyperspectral data for new generation sensors

This paper addresses lossy compression of hyperspectral images acquired by sensors of new generation for which signaldependent component of the noise is prevailing compared to the noise-independent component. First, for sub-band (component-wise) compression, it is shown that there can exist an optimal operation point (OOP) for which MSE between compressed and noise-free image is minimal, i.e., maximal noise filtering effect is observed. This OOP can be observed for two approaches to lossy compression where the first one presumes direct application of a coder to original data and the second approach deals with applying direct and inverse variance stabilizing transform (VST). Second, it is demonstrated that the second approach is preferable since it usually provides slightly smaller MSE and slightly larger compression ratio (CR) in OOP. One more advantage of the second approach is that the coder parameter that controls CR can be set fixed for all sub-band images. Moreover, CR can be considerably (approximately twice) increased if sub-band images after VST are grouped and lossy compression is applied to a first sub-band image in a group and to “difference” images obtained for this group. The proposed approach is tested for Hyperion hyperspectral images and shown to provide CR about 15 for data compression in the neighborhood of OOP.

Blind estimation of blur in hyperspectral images

Hyperspectral images acquired by remote sensing systems are generally degraded by noise and can be sometimes more severely degraded by blur. When no knowledge is available about the degradations present on the original image, blind restoration methods can only be considered. By blind, we mean absolutely no knowledge neither of the blur point spread function (PSF) nor the original latent channel and the noise level. In this study, we address the blind restoration of the degraded channels component-wise, according to a sequential scheme. For each degraded channel, the sequential scheme estimates the blur point spread function (PSF) in a first stage and deconvolves the degraded channel in a second and final stage by means of using the PSF previously estimated. We propose a new component-wise blind method for estimating effectively and accurately the blur point spread function. This method follows recent approaches suggesting the detection, selection and use of sufficiently salient edges in the current processed channel for supporting the regularized blur PSF estimation. Several modifications are beneficially introduced in our work. A new selection of salient edges through thresholding adequately the cumulative distribution of their corresponding gradient magnitudes is introduced. Besides, quasi-automatic and spatially adaptive tuning of the involved regularization parameters is considered. To prove applicability and higher efficiency of the proposed method, we compare it against the method it originates from and four representative edge-sparsifying regularized methods of the literature already assessed in a previous work. Our attention is mainly paid to the objective analysis (via ݈l1-norm) of the blur PSF error estimation accuracy. The tests are performed on a synthetic hyperspectral image. This synthetic hyperspectral image has been built from various samples from classified areas of a real-life hyperspectral image, in order to benefit from realistic spatial distribution of reference spectral signatures to recover after synthetic degradation. The synthetic hyperspectral image has been successively degraded with eight real blurs taken from the literature, each of a different support size. Conclusions, practical recommendations and perspectives are drawn from the results experimentally obtained.

Accuracy assessment of blind and semi-blind restoration methods for hyperspectral images

Hyperspectral images acquired by remote sensing systems are generally degraded by noise and can be sometimes more severely degraded by blur. When no knowledge is available about the degradations present or the original image, blind restoration methods must be considered. Otherwise, when a partial information is needed, semi-blind restoration methods can be considered. Numerous semi-blind and quite advanced methods are available in the literature. So to get better insights and feedback on the applicability and potential efficiency of a representative set of four semi-blind methods recently proposed, we have performed a comparative study of these methods in objective terms of blur filter and original image error estimation accuracy. In particular, we have paid special attention to the accurate recovering in the spectral dimension of original spectral signatures. We have analyzed peculiarities and factors restricting the applicability of these methods. Our tests are performed on a synthetic hyperspectral image, degraded with various synthetic blurs (out-of-focus, gaussian, motion) and with signal independent noise of typical levels such as those encountered in real hyperspectral images. This synthetic image has been built from various samples from classified areas of a real-life hyperspectral image, in order to benefit from realistic reference spectral signatures to recover after synthetic degradation. Conclusions, practical recommendations and perspectives are drawn from the results experimentally obtained.

Denoising efficiency for multichannel images corrupted by signal-dependent noise

Essential improvements in quality of original images formed by multichannel (multi- and hyperspectral) sensors have been gained in recent years. In particular, level of thermal noise in acquired images has been sufficiently reduced [1]. However, there are still component (sub-band) images in obtained data for which noise level is quite high [2, 3]. One more peculiarity is that signal-dependent noise component is characterized by dominant contribution [3] for new generation of sensors. Sometimes, the component images with the lowest signal-to-noise ratio (SNR) are ignored at stages of multichannel image classification and interpreting [1, 2]. However, recent studies have demonstrated that useful information can be extracted from “noisy” sub-band images under condition that noise is reduced by an efficient pre-filtering technique [2]. Thus, an actual task is to design such efficient techniques able to cope with signal-dependent noise and to analyze their performance.

Non-parametric detection scheme for isotropic image texture with normal increments

We analyze applicability of 2D fractal Brownian motion (fBm) for real-life image textures with respect to two general fBm properties: isotropy and normality of its increments. A non-parametric detection scheme for texture satisfying these two properties is proposed. It is based on Lilliefors test for texture increments normality and Kolmogorov-Smirnov two samples test for equality of distributions of pairs of increments. The scheme is tested against large real-life images database and is shown to detect and remove such image patterns as edges, areas with clipping effects, irregular and anisotropic textures.

NoiseNet: Signal-Dependent Noise Variance Estimation with Convolutional Neural Network

In this paper, the problem of blind estimation of uncorrelated signal-dependent noise parameters in images is formulated as a regression problem with uncertainty. It is shown that this regression task can be effectively solved by a properly trained deep convolution neural network (CNN), called NoiseNet, comprising regressor branch and uncertainty quantifier branch. The former predicts noise standard deviation (STD) for a 32 \(\times \) 32 pixels image patch, while the latter predicts STD of regressor error. The NoiseNet architecture is proposed and peculiarities of its training are discussed. Signal-dependent noise parameters are estimated by robust iterative processing of many local estimates provided by the NoiseNet. The comparative analysis for real data from NED2012 database is carried out. Its results show that the NoiseNet provides accuracy better than the state-of-the-art existing methods.

Towards a blind restoration method of hyperspectral images

Image restoration is a necessary stage in the processing of remotely sensed hyperspectral images, when they are severely degraded by blur and noise. We address the semi-blind restoration of such degraded images component-wise, according to a sequential scheme. By semi-blind, we mean introducing a minimum of a priori knowledge on main unknowns in the restoration process. For each degraded component image, main unknowns are the point spread function of the blur, the original component image and the noise level. Then, the sequential component-wise scheme amounts in a first stage to estimating the blur point spread function directly from the considered degraded component image and in a second and final stage, deconvolving the degraded channel by using the PSF previously estimated. Our contribution is to improve further the sequential component-wise semi-blind variants of a recently proposed method. In this work, modifications previously introduced separately are applied all together. All these modifications together are beneficial as they tend to make the newly proposed method as independent as possible of the data content and their degradations. The resulting method is experimentally compared against its original version and the best ADMM-based alternative found experimentally in previous works. The tests are performed on three real Specim-AISA-Eagle hyperspectral images. The component images of these images are degraded synthetically with eight real and arbitrary blurs. Our attention is mainly paid to the objective analysis of the l1-norm of the estimation errors. Experimental results of this comparative analysis show that the newly proposed method exhibits interesting competitive performances and can outperform the methods involved in the experimental comparison.

Analysis of signal-dependent sensor noise on JPEG 2000-compressed Sentinel-2 multi-spectral images

The processing chain of Sentinel-2 MultiSpectral Instrument (MSI) data involves filtering and compression stages that modify MSI sensor noise. As a result, noise in Sentinel-2 Level-1C data distributed to users becomes processed. We demonstrate that processed noise variance model is bivariate: noise variance depends on image intensity (caused by signal-dependency of photon counting detectors) and signal-to-noise ratio (SNR; caused by filtering/compression). To provide information on processed noise parameters, which is missing in Sentinel-2 metadata, we propose to use blind noise parameter estimation approach. Existing methods are restricted to univariate noise model. Therefore, we propose extension of existing vcNI+fBm blind noise parameter estimation method to multivariate noise model, mvcNI+fBm, and apply it to each band of Sentinel-2A data. Obtained results clearly demonstrate that noise variance is affected by filtering/compression for SNR less than about 15. Processed noise variance is reduced by a factor of 2 - 5 in homogeneous areas as compared to noise variance for high SNR values. Estimate of noise variance model parameters are provided for each Sentinel-2A band. Sentinel-2A MSI Level-1C noise models obtained in this paper could be useful for end users and researchers working in a variety of remote sensing applications.