16 research outputs found

    Bayesian inverse problems

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    We consider linear, mildly ill-posed inverse problems in separable Hilbert spaces under Gaussian noise, whose covariance operator is not identity (i.e. it is not a white noise problem), and use the Bayesian approach to nd their regularised solution. Speci cally, our goal is to regularise the prior in such a way that the posterior distribution achieves the optimal rate of contraction. The object of interest (an unknown function) is assumed to lie in a Sobolev space. Firstly, we consider the so-called conjugate setting where the covariance operator of the noise and the covariance operator of the prior are simultaneously diagonalisable, and the noise has heterogeneous variance. Note this similar to the work done in [Knapik et al., 2011], albeit for the homogeneous variance case. Hence, we derive the minimax rate of convergence, the contraction rate of the posterior distribution and subsequently, discuss the conditions under which these rates coincide. The results are numerically illustrated by the problem of recovering a function from noisy observations. Secondly, motivated by Poisson inverse problems, we consider Gaussian, signaldependent noise (i.e. non-conjugate setting). Using [Panov and Spokoiny, 2015] we obtain Bernstein von-Mises results for the posterior distribution, and consequently derive the contraction rates and conditions for its optimality as well

    Structure-aware image denoising, super-resolution, and enhancement methods

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    Denoising, super-resolution and structure enhancement are classical image processing applications. The motive behind their existence is to aid our visual analysis of raw digital images. Despite tremendous progress in these fields, certain difficult problems are still open to research. For example, denoising and super-resolution techniques which possess all the following properties, are very scarce: They must preserve critical structures like corners, should be robust to the type of noise distribution, avoid undesirable artefacts, and also be fast. The area of structure enhancement also has an unresolved issue: Very little efforts have been put into designing models that can tackle anisotropic deformations in the image acquisition process. In this thesis, we design novel methods in the form of partial differential equations, patch-based approaches and variational models to overcome the aforementioned obstacles. In most cases, our methods outperform the existing approaches in both quality and speed, despite being applicable to a broader range of practical situations.Entrauschen, Superresolution und Strukturverbesserung sind klassische Anwendungen der Bildverarbeitung. Ihre Existenz bedingt sich in dem Bestreben, die visuelle Begutachtung digitaler Bildrohdaten zu unterstützen. Trotz erheblicher Fortschritte in diesen Feldern bedürfen bestimmte schwierige Probleme noch weiterer Forschung. So sind beispielsweise Entrauschungsund Superresolutionsverfahren, welche alle der folgenden Eingenschaften besitzen, sehr selten: die Erhaltung wichtiger Strukturen wie Ecken, Robustheit bezüglich der Rauschverteilung, Vermeidung unerwünschter Artefakte und niedrige Laufzeit. Auch im Gebiet der Strukturverbesserung liegt ein ungelöstes Problem vor: Bisher wurde nur sehr wenig Forschungsaufwand in die Entwicklung von Modellen investieret, welche anisotrope Deformationen in bildgebenden Verfahren bewältigen können. In dieser Arbeit entwerfen wir neue Methoden in Form von partiellen Differentialgleichungen, patch-basierten Ansätzen und Variationsmodellen um die oben erwähnten Hindernisse zu überwinden. In den meisten Fällen übertreffen unsere Methoden nicht nur qualitativ die bisher verwendeten Ansätze, sondern lösen die gestellten Aufgaben auch schneller. Zudem decken wir mit unseren Modellen einen breiteren Bereich praktischer Fragestellungen ab

    Enhancing Patch-Based Methods with Inter-frame Connectivity for Denoising Multi-frame Images

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    The 3D block matching (BM3D) method is among the state-of-art methods for denoising images corrupted with additive white Gaussian noise. With the help of a novel inter-frame connectivity strategy, we propose an extension of the BM3D method for the scenario where we have multiple images of the same scene. Our proposed extension outperforms all the existing trivial and non-trivial extensions of patch-based denoising methods for multi-frame images. We can achieve a quality difference of as high as 28% over the next best method without using any additional parameters. Our method can also be easily generalised to other similar existing patch-based methods

    Sensor noise measurement in the presence of a flickering illumination

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    International audienceRaw data from a digital imaging sensor are impaired by a heteroscedastic noise, the variance of pixel intensity linearly depending on the expected value. The most natural way of estimating the variance and the expected value at a given pixel is certainly empirical estimation from the variations along a stack of images of any static scene acquired at different times under the same camera setting. However, the relation found between the sample variance and the sample expectation is actually not linear, especially in the presence of a flickering illumination. The contribution of this paper is twofold. First, a theoretical model of this phenomenon shows that the linear relation changes into a quadratic one. Second, an algorithm is designed, which not only gives the parameters of the expected linear relation, but also the whole set of parameters governing an image formation, namely the gain, the offset and the readout noise. The rolling shutter effect is also considered

    Sensor Noise Modeling by Stacking Pseudo-Periodic Grid Images Affected by Vibrations

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    International audienceThis letter addresses the problem of noise estimation in raw images from digital sensors. Assuming that a series of images of a static scene are available, a possibility is to characterize the noise at a given pixel by considering the random fluctuations of the gray level across the images. However, mechanical vibrations, even tiny ones, affect the experimental setup, making this approach ineffective. The contribution of this letter is twofold. It is shown that noise estimation in the presence of vibrations is actually biased. Focusing on images of a pseudo-periodic grid, an algorithm to discard their effect is also given. An application to the generalized Anscombe transform is discussed

    Effect of Sensor Noise on the Resolution and Spatial Resolution of Displacement and Strain Maps Estimated with the Grid Method

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    International audienceThis paper deals with noise propagation from camera sensor to displacement and strain maps when the grid method is employed to estimate these quantities. It is shown that closed-form equations can be employed to predict the link between metrological characteristics such as resolution and spatial resolution in displacement and strain maps on the one hand and various quantities characterising grid images such as brightness, contrast and standard deviation of noise on the other hand. Various numerical simulations confirm first the relevance of this approach in the case of an idealised camera sensor impaired by a homoscedastic Gaussian white noise. Actual CCD or CMOS sensors exhibit, however, a heteroscedastic noise. A pre-processing step is therefore proposed to first stabilise noise variance prior to employing the predictive equations, which provide the resolution in strain and displacement maps due to sensor noise. This step is based on both a modelling of sensor noise and the use of the generalised Anscombe transform to stabilise noise variance. Applying this procedure in the case of a translation test confirms that it is possible to model correctly noise propagation from sensor to displacement and strain maps, and thus also to predict the actual link between resolution, spatial resolution and standard deviation of noise in grid images

    A CANDLE for a deeper in-vivo insight

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    A new Collaborative Approach for eNhanced Denoising under Low-light Excitation (CANDLE) is introduced for the processing of 3D laser scanning multiphoton microscopy images. CANDLE is designed to be robust for low signal-to-noise ratio (SNR) conditions typically encountered when imaging deep in scattering biological specimens. Based on an optimized non-local means filter involving the comparison of filtered patches, CANDLE locally adapts the amount of smoothing in order to deal with the noise inhomogeneity inherent to laser scanning fluorescence microscopy images. An extensive validation on synthetic data, images acquired on microspheres and in vivo images is presented. These experiments show that the CANDLE filter obtained competitive results compared to a state-of-the-art method and a locally adaptive optimized non-local means filter, especially under low SNR conditions (PSNR < 8 dB). Finally, the deeper imaging capabilities enabled by the proposed filter are demonstrated on deep tissue in vivo images of neurons and fine axonal processes in the Xenopus tadpole brain.We want to thank Florian Luisier for providing free plugin of his PureDenoise filter. We also want to thank Markku Makitalo for providing the code of their OVST. This study was supported by the Canadian Institutes of Health Research (CIHR, MOP-84360 to DLC and MOP-77567 to ESR) and Cda (CECR)-Gevas-OE016. MM holds a fellowship from the Deutscher Akademischer Austasch Dienst (DAAD) and a McGill Principal's Award. ESR is a tier 2 Canada Research Chair. This work has been partially supported by the Spanish Health Institute Carlos III through the RETICS Combiomed, RD07/0067/2001. This work benefited from the use of ImageJ.Coupé, P.; Munz, M.; Manjón Herrera, JV.; Ruthazer, ES.; Collins, DL. (2012). A CANDLE for a deeper in-vivo insight. Medical Image Analysis. 16(4):849-864. https://doi.org/10.1016/j.media.2012.01.002S84986416

    Poisson-Gaussian noise parameter estimation in fluorescence microscopy imaging

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    International audienceIn this paper, we present a new fully automatic approach for noise parameter estimation in the context of fluorescence imaging systems. In particular, we address the problem of Poisson-Gaussian noise modeling in the nonstationary case. In microscopy practice, the nonstationarity is due to the photobleaching effect. The proposed method consists of an adequate moment based initialization followed by Expectation-Maximization iterations. This approach is shown to provide reliable estimates of the mean and the variance of the Gaussian noise and of the scale parameter of Poisson noise, as well as of the photobleaching rates. The algorithm performance is demonstrated on both synthetic and real fluorescence microscopy image sequences
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