Enhancement and Restoration of Microscopic Images Corrupted with Poisson's Noise Using a Nonlinear Partial Differential Equation-based Filter

An inherent characteristic of the many imaging modalities such as fluorescence microscopy and other microscopic modalities is the presence of intrinsic Poisson noise that may lead to degradation of the captured image during its formation. A nonlinear complex diffusion-based filter adapted to Poisson noise is proposed in this paper to restore and enhance the degraded microscopic images captured by imaging devices having photon limited light detectors. The proposed filter is based on a maximum a posterior approach to the image reconstruction problem. The formulation of the filtering problem as maximisation of a posterior is useful because it allows one to incorporate the Poisson likelihood term as a data attachment which can be added to an image prior model. Here, the Gibb's image prior model-based on energy functional defined in terms of gradient norm of the image is used. The performance of the proposed scheme has been compared with other standard techniques available in literature such as Wiener filter, regularised filter, Lucy-Richardson filter and another proposed nonlinear anisotropic diffusion-based filter in terms of mean square error, peak signal-to-noise ratio, correlation parameter and mean structure similarity index map.The results shows that the proposed complex diffusion-based filter adapted to Poisson noise performs better in comparison to other filters and is better choice for reduction of intrinsic Poisson noise from the digital microscopic images and it is also well capable of preserving edges and radiometric information such as luminance and contrast of the restored image.Defence Science Journal, 2011, 61(5), pp.452-461, DOI:http://dx.doi.org/10.14429/dsj.61.118

Inferring Latent States and Refining Force Estimates via Hierarchical Dirichlet Process Modeling in Single Particle Tracking Experiments

Optical microscopy provides rich spatio-temporal information characterizing in vivo molecular motion. However, effective forces and other parameters used to summarize molecular motion change over time in live cells due to latent state changes, e.g., changes induced by dynamic micro-environments, photobleaching, and other heterogeneity inherent in biological processes. This study focuses on techniques for analyzing Single Particle Tracking (SPT) data experiencing abrupt state changes. We demonstrate the approach on GFP tagged chromatids experiencing metaphase in yeast cells and probe the effective forces resulting from dynamic interactions that reflect the sum of a number of physical phenomena. State changes are induced by factors such as microtubule dynamics exerting force through the centromere, thermal polymer fluctuations, etc. Simulations are used to demonstrate the relevance of the approach in more general SPT data analyses. Refined force estimates are obtained by adopting and modifying a nonparametric Bayesian modeling technique, the Hierarchical Dirichlet Process Switching Linear Dynamical System (HDP-SLDS), for SPT applications. The HDP-SLDS method shows promise in systematically identifying dynamical regime changes induced by unobserved state changes when the number of underlying states is unknown in advance (a common problem in SPT applications). We expand on the relevance of the HDP-SLDS approach, review the relevant background of Hierarchical Dirichlet Processes, show how to map discrete time HDP-SLDS models to classic SPT models, and discuss limitations of the approach. In addition, we demonstrate new computational techniques for tuning hyperparameters and for checking the statistical consistency of model assumptions directly against individual experimental trajectories; the techniques circumvent the need for "ground-truth" and subjective information.Comment: 25 pages, 6 figures. Differs only typographically from PLoS One publication available freely as an open-access article at http://journals.plos.org/plosone/article?id=10.1371/journal.pone.013763

Denoising 3D microscopy images of cell nuclei using shape priors on an anisotropic grid

This paper presents a new multiscale method to denoise three-dimensional images of cell nuclei. The speci- ficity of this method is its awareness of the noise distribution and object shapes. It combines a multiscale representation called Isotropic Undecimated Wavelet Transform (IUWT) with a nonlinear transform, a statistical test and a variational method, to retrieve spherical shapes in the image. Beyond extending an existing 2D approach to a 3D problem, our algorithm takes the sampling grid dimensions into account. We compare our method to the two algorithms from which it is derived on a representative image analysis task, and show that it is superior to both of them. It brings a slight improvement in the signal-to-noise ratio and a significant improvement in cell detection

Feature-preserving image restoration and its application in biological fluorescence microscopy

This thesis presents a new investigation of image restoration and its application to fluorescence cell microscopy. The first part of the work is to develop advanced image denoising algorithms to restore images from noisy observations by using a novel featurepreserving diffusion approach. I have applied these algorithms to different types of images, including biometric, biological and natural images, and demonstrated their superior performance for noise removal and feature preservation, compared to several state of the art methods. In the second part of my work, I explore a novel, simple and inexpensive super-resolution restoration method for quantitative microscopy in cell biology. In this method, a super-resolution image is restored, through an inverse process, by using multiple diffraction-limited (low) resolution observations, which are acquired from conventional microscopes whilst translating the sample parallel to the image plane, so referred to as translation microscopy (TRAM). A key to this new development is the integration of a robust feature detector, developed in the first part, to the inverse process to restore high resolution images well above the diffraction limit in the presence of strong noise. TRAM is a post-image acquisition computational method and can be implemented with any microscope. Experiments show a nearly 7-fold increase in lateral spatial resolution in noisy biological environments, delivering multi-colour image resolution of ~30 nm

3D + t Morphological Processing: Applications to Embryogenesis Image Analysis

We propose to directly process 3D + t image sequences with mathematical morphology operators, using a new classi?cation of the 3D+t structuring elements. Several methods (?ltering, tracking, segmentation) dedicated to the analysis of 3D + t datasets of zebra?sh embryogenesis are introduced and validated through a synthetic dataset. Then, we illustrate the application of these methods to the analysis of datasets of zebra?sh early development acquired with various microscopy techniques. This processing paradigm produces spatio-temporal coherent results as it bene?ts from the intrinsic redundancy of the temporal dimension, and minimizes the needs for human intervention in semi-automatic algorithms

Particle tracking and inference in fluorescence microscopy

Observing biophysical phenomena at the nanometer scale with both high spatial and temporal resolution is a challenging feat. Although many techniques, including atomic force microscopy and scanning electron microscopy, have demonstrated subnanometer spatial resolution, most exhibit drawbacks which limit their temporal resolution. On the other hand, light microscopy exhibits poor spatial resolution (typically greater than 100 nm) due to diffraction. The desire to image features below the resolution of light has spawned the term super-resolution microscopy to which many powerful, albeit complicated, techniques may be associated; such techniques include Stimulated Emission-Depletion Microscopy (STED) and Stochastic Optical Reconstruction Microscopy (STORM). Within the field of super-resolution there exists a subset of methods which involve tagging features of interest (e.g., a virus or motor protein) with small, fluorescent molecules and measuring their emitted fluorescence over time. Although the emitted light is diffraction-limited, the precision of localizing the position of the molecule is proportional to the number of photons acquired. Thus, fluorescent particle tracking is a method which augments traditional light microscopy so that features may be localized to spatial resolutions below the diffraction limit while still maintaining useful temporal resolutions. One common approach for tracking fluorescent particles involves passively observing the particle with a stationary detector; this approach, however, is limited by its inability to observe particles in three dimensions over a large field of view. Consequently, specialized techniques have been developed that actively track the particle, but the majority of these methods, unfortunately, utilize non-standard optical paths which complicate their use. Moreover, analysis methods pertaining to both paradigms, which infer both position locations and model-based parameter estimates, are often subjective or employ simplified and potentially inaccurate models. In widefield microscopy, for example, the common approach involves first localizing the particle within each image via a heuristic method, such as calculating the centroid, and then inferring diffusion coefficients by regressing to the mean squared displacement. This approach to localization disregards information involving the optical setup (e.g., the point spread function, aberrations, and noise) as well as information regarding the particle's motion. Although methods exist for optimally calculating diffusion coefficients, they are limited to the case of unconfined diffusion with measurements corrupted by additive, white noise. The work in this thesis provides two specific contributions. The first presents an active approach to tracking a single fluorescent particle in three dimensions that requires no specialized hardware aside from a standard confocal microscope. Inspired by works involving the autonomous exploration of unknown potential fields, the algorithm operates by moving the microscope's focal volume toward the maximum of the field of light emitted by the particle. For a stationary particle and a radial field, an equilibrium trajectory is derived and its local stability is proven. In addition, the algorithm's ability to track both stationary and diffusive particles is numerically characterized. The second contribution presents the application of a numerical, iterative algorithm to the problem of simultaneously inferring both location and model parameters from particle tracking data of potentially nonlinear and non-Gaussian imaging modalities. The method, which is leveraged from the field of system identification, employs Sequential Monte Carlo methods in conjunction with the Expectation Maximization algorithm to provide approximate maximum likelihood estimates of model parameters (e.g., diffusion coefficients) as well as approximate posterior probability densities of the particle's location over time. The effectiveness of the method is demonstrated through numerical simulations of two- and three-dimensional motion (including free, confined, and tethered diffusion) imaged in a widefield context. Lastly, the effectiveness of both methods is demonstrated by tracking a quantum dot in a hydrogel with the proposed tracking method and by analyzing the resulting data using the aforementioned inference method

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

Fluorescence microscopy: Established and emerging methods, experimental strategies, and applications in immunology

Cutting-edge biophysical technologies including total internal reflection fluorescence microscopy, single molecule fluorescence, single channel opening events, fluorescence resonance energy transfer, high-speed exposures, two-photon imaging, fluorescence lifetime imaging, and other tools are becoming increasingly important in immunology as they link molecular events to cellular physiology, a key goal of modern immunology. The primary concern in all forms of microscopy is the generation of contrast; for fluorescence microscopy contrast can be thought of as the difference in intensity between the cell and background, the signal-to-noise ratio. High information-content images can be formed by enhancing the signal, suppressing the noise, or both. As improved tools, such as ICCD and EMCCD cameras, become available for fluorescence imaging in molecular and cellular immunology, it is important to optimize other aspects of the imaging system. Numerous practical strategies to enhance fluorescence microscopy experiments are reviewed. The use of instrumentation such as light traps, cameras, objectives, improved fluorescent labels, and image filtration routines applicable to low light level experiments are discussed. New methodologies providing resolution well beyond that given by the Rayleigh criterion are outlined. Ongoing and future developments in fluorescence microscopy instrumentation and technique are reviewed. This review is intended to address situations where the signal is weak, which is important for emerging techniques stressing super-resolution or live cell dynamics, but is less important for conventional applications such as indirect immunofluorescence. This review provides a broad integrative discussion of fluorescence microscopy with selected applications in immunology. Microsc. Res. Tech., 2007. © 2007 Wiley-Liss, Inc.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/56150/1/20455_ftp.pd