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

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

Adaptive Edge-guided Block-matching and 3D filtering (BM3D) Image Denoising Algorithm

Image denoising is a well studied field, yet reducing noise from images is still a valid challenge. Recently proposed Block-matching and 3D filtering (BM3D) is the current state of the art algorithm for denoising images corrupted by Additive White Gaussian noise (AWGN). Though BM3D outperforms all existing methods for AWGN denoising, still its performance decreases as the noise level increases in images, since it is harder to find proper match for reference blocks in the presence of highly corrupted pixel values. It also blurs sharp edges and textures. To overcome these problems we proposed an edge guided BM3D with selective pixel restoration. For higher noise levels it is possible to detect noisy pixels form its neighborhoods gray level statistics. We exploited this property to reduce noise as much as possible by applying a pre-filter. We also introduced an edge guided pixel restoration process in the hard-thresholding step of BM3D to restore the sharpness of edges and textures. Experimental results confirm that our proposed method is competitive and outperforms the state of the art BM3D in all considered subjective and objective quality measurements, particularly in preserving edges, textures and image contrast

The SURE-LET approach to image denoising

Denoising is an essential step prior to any higher-level image-processing tasks such as segmentation or object tracking, because the undesirable corruption by noise is inherent to any physical acquisition device. When the measurements are performed by photosensors, one usually distinguish between two main regimes: in the first scenario, the measured intensities are sufficiently high and the noise is assumed to be signal-independent. In the second scenario, only few photons are detected, which leads to a strong signal-dependent degradation. When the noise is considered as signal-independent, it is often modeled as an additive independent (typically Gaussian) random variable, whereas, otherwise, the measurements are commonly assumed to follow independent Poisson laws, whose underlying intensities are the unknown noise-free measures. We first consider the reduction of additive white Gaussian noise (AWGN). Contrary to most existing denoising algorithms, our approach does not require an explicit prior statistical modeling of the unknown data. Our driving principle is the minimization of a purely data-adaptive unbiased estimate of the mean-squared error (MSE) between the processed and the noise-free data. In the AWGN case, such a MSE estimate was first proposed by Stein, and is known as "Stein's unbiased risk estimate" (SURE). We further develop the original SURE theory and propose a general methodology for fast and efficient multidimensional image denoising, which we call the SURE-LET approach. While SURE allows the quantitative monitoring of the denoising quality, the flexibility and the low computational complexity of our approach are ensured by a linear parameterization of the denoising process, expressed as a linear expansion of thresholds (LET).We propose several pointwise, multivariate, and multichannel thresholding functions applied to arbitrary (in particular, redundant) linear transformations of the input data, with a special focus on multiscale signal representations. We then transpose the SURE-LET approach to the estimation of Poisson intensities degraded by AWGN. The signal-dependent specificity of the Poisson statistics leads to the derivation of a new unbiased MSE estimate that we call "Poisson's unbiased risk estimate" (PURE) and requires more adaptive transform-domain thresholding rules. In a general PURE-LET framework, we first devise a fast interscale thresholding method restricted to the use of the (unnormalized) Haar wavelet transform. We then lift this restriction and show how the PURE-LET strategy can be used to design and optimize a wide class of nonlinear processing applied in an arbitrary (in particular, redundant) transform domain. We finally apply some of the proposed denoising algorithms to real multidimensional fluorescence microscopy images. Such in vivo imaging modality often operates under low-illumination conditions and short exposure time; consequently, the random fluctuations of the measured fluorophore radiations are well described by a Poisson process degraded (or not) by AWGN. We validate experimentally this statistical measurement model, and we assess the performance of the PURE-LET algorithms in comparison with some state-of-the-art denoising methods. Our solution turns out to be very competitive both qualitatively and computationally, allowing for a fast and efficient denoising of the huge volumes of data that are nowadays routinely produced in biomedical imaging

Unraveling the Thousand Word Picture: An Introduction to Super-Resolution Data Analysis

Super-resolution microscopy provides direct insight into fundamental biological processes occurring at length scales smaller than light’s diffraction limit. The analysis of data at such scales has brought statistical and machine learning methods into the mainstream. Here we provide a survey of data analysis methods starting from an overview of basic statistical techniques underlying the analysis of super-resolution and, more broadly, imaging data. We subsequently break down the analysis of super-resolution data into four problems: the localization problem, the counting problem, the linking problem, and what we’ve termed the interpretation problem

Filter-Based Probabilistic Markov Random Field Image Priors: Learning, Evaluation, and Image Analysis

Markov random fields (MRF) based on linear filter responses are one of the most popular forms for modeling image priors due to their rigorous probabilistic interpretations and versatility in various applications. In this dissertation, we propose an application-independent method to quantitatively evaluate MRF image priors using model samples. To this end, we developed an efficient auxiliary-variable Gibbs samplers for a general class of MRFs with flexible potentials. We found that the popular pairwise and high-order MRF priors capture image statistics quite roughly and exhibit poor generative properties. We further developed new learning strategies and obtained high-order MRFs that well capture the statistics of the inbuilt features, thus being real maximum-entropy models, and other important statistical properties of natural images, outlining the capabilities of MRFs. We suggest a multi-modal extension of MRF potentials which not only allows to train more expressive priors, but also helps to reveal more insights of MRF variants, based on which we are able to train compact, fully-convolutional restricted Boltzmann machines (RBM) that can model visual repetitive textures even better than more complex and deep models. The learned high-order MRFs allow us to develop new methods for various real-world image analysis problems. For denoising of natural images and deconvolution of microscopy images, the MRF priors are employed in a pure generative setting. We propose efficient sampling-based methods to infer Bayesian minimum mean squared error (MMSE) estimates, which substantially outperform maximum a-posteriori (MAP) estimates and can compete with state-of-the-art discriminative methods. For non-rigid registration of live cell nuclei in time-lapse microscopy images, we propose a global optical flow-based method. The statistics of noise in fluorescence microscopy images are studied to derive an adaptive weighting scheme for increasing model robustness. High-order MRFs are also employed to train image filters for extracting important features of cell nuclei and the deformation of nuclei are then estimated in the learned feature spaces. The developed method outperforms previous approaches in terms of both registration accuracy and computational efficiency

Adaptive Nonlocal Signal Restoration and Enhancement Techniques for High-Dimensional Data

The large number of practical applications involving digital images has motivated a significant interest towards restoration solutions that improve the visual quality of the data under the presence of various acquisition and compression artifacts. Digital images are the results of an acquisition process based on the measurement of a physical quantity of interest incident upon an imaging sensor over a specified period of time. The quantity of interest depends on the targeted imaging application. Common imaging sensors measure the number of photons impinging over a dense grid of photodetectors in order to produce an image similar to what is perceived by the human visual system. Different applications focus on the part of the electromagnetic spectrum not visible by the human visual system, and thus require different sensing technologies to form the image. In all cases, even with the advance of technology, raw data is invariably affected by a variety of inherent and external disturbing factors, such as the stochastic nature of the measurement processes or challenging sensing conditions, which may cause, e.g., noise, blur, geometrical distortion and color aberration. In this thesis we introduce two filtering frameworks for video and volumetric data restoration based on the BM3D grouping and collaborative filtering paradigm. In its general form, the BM3D paradigm leverages the correlation present within a nonlocal emph{group} composed of mutually similar basic filtering elements, e.g., patches, to attain an enhanced sparse representation of the group in a suitable transform domain where the energy of the meaningful part of the signal can be thus separated from that of the noise through coefficient shrinkage. We argue that the success of this approach largely depends on the form of the used basic filtering elements, which in turn define the subsequent spectral representation of the nonlocal group. Thus, the main contribution of this thesis consists in tailoring specific basic filtering elements to the the inherent characteristics of the processed data at hand. Specifically, we embed the local spatial correlation present in volumetric data through 3-D cubes, and the local spatial and temporal correlation present in videos through 3-D spatiotemporal volumes, i.e. sequences of 2-D blocks following a motion trajectory. The foundational aspect of this work is the analysis of the particular spectral representation of these elements. Specifically, our frameworks stack mutually similar 3-D patches along an additional fourth dimension, thus forming a 4-D data structure. By doing so, an effective group spectral description can be formed, as the phenomena acting along different dimensions in the data can be precisely localized along different spectral hyperplanes, and thus different filtering shrinkage strategies can be applied to different spectral coefficients to achieve the desired filtering results. This constitutes a decisive difference with the shrinkage traditionally employed in BM3D-algorithms, where different hyperplanes of the group spectrum are shrunk subject to the same degradation model. Different image processing problems rely on different observation models and typically require specific algorithms to filter the corrupted data. As a consequent contribution of this thesis, we show that our high-dimensional filtering model allows to target heterogeneous noise models, e.g., characterized by spatial and temporal correlation, signal-dependent distributions, spatially varying statistics, and non-white power spectral densities, without essential modifications to the algorithm structure. As a result, we develop state-of-the-art methods for a variety of fundamental image processing problems, such as denoising, deblocking, enhancement, deflickering, and reconstruction, which also find practical applications in consumer, medical, and thermal imaging

Review : Deep learning in electron microscopy

Deep learning is transforming most areas of science and technology, including electron microscopy. This review paper offers a practical perspective aimed at developers with limited familiarity. For context, we review popular applications of deep learning in electron microscopy. Following, we discuss hardware and software needed to get started with deep learning and interface with electron microscopes. We then review neural network components, popular architectures, and their optimization. Finally, we discuss future directions of deep learning in electron microscopy