Parametric Blind Deconvolution for Confocal Laser Scanning Microscopy (CLSM)-Proof of Concept

We propose a method for the iterative restoration of fluorescence Confocal Laser Scanning Microscope (CLSM) images with parametric estimation of the acquisition system's Point Spread Function (PSF). The CLSM is an optical fluorescence microscope that scans a specimen in 3D and uses a pinhole to reject most of the out-of-focus light. However, the quality of the image suffers from two primary physical limitations. The first is due to the diffraction-limited nature of the optical system and the second is due to the reduced amount of light detected by the photomultiplier tube (PMT). These limitations cause blur and photon counting noise respectively. The images can hence benefit from post-processing restoration methods based on deconvolution. An efficient method for parametric blind image deconvolution involves the simultaneous estimation of the specimen 3D distribution of fluorescent sources and the microscope PSF. By using a model for the microscope image acquisition physical process, we reduce the number of free parameters describing the PSF and introduce constraints. The parameters of the PSF may vary during the course of experimentation, and so they have to be estimated directly from the observation data. We also introduce a priori knowledge of the specimen that permits stabilization of the estimation process and favorizes the convergence. Experiments on simulated data show that the PSF could be estimatedwith a higher degree of accuracy and those done on real data show very good deconvolution results in comparison to the theoretical microscope PSF model

Testing for lack of fit in inverse regression - with applications to photonic imaging.

Regression; Problems; Lack-of-fit; Applications;

Bayesian image restoration and bacteria detection in optical endomicroscopy

Optical microscopy systems can be used to obtain high-resolution microscopic images of tissue cultures and ex vivo tissue samples. This imaging technique can be translated for in vivo, in situ applications by using optical fibres and miniature optics. Fibred optical endomicroscopy (OEM) can enable optical biopsy in organs inaccessible by any other imaging systems, and hence can provide rapid and accurate diagnosis in a short time. The raw data the system produce is difficult to interpret as it is modulated by a fibre bundle pattern, producing what is called the “honeycomb effect”. Moreover, the data is further degraded due to the fibre core cross coupling problem. On the other hand, there is an unmet clinical need for automatic tools that can help the clinicians to detect fluorescently labelled bacteria in distal lung images. The aim of this thesis is to develop advanced image processing algorithms that can address the above mentioned problems. First, we provide a statistical model for the fibre core cross coupling problem and the sparse sampling by imaging fibre bundles (honeycomb artefact), which are formulated here as a restoration problem for the first time in the literature. We then introduce a non-linear interpolation method, based on Gaussian processes regression, in order to recover an interpretable scene from the deconvolved data. Second, we develop two bacteria detection algorithms, each of which provides different characteristics. The first approach considers joint formulation to the sparse coding and anomaly detection problems. The anomalies here are considered as candidate bacteria, which are annotated with the help of a trained clinician. Although this approach provides good detection performance and outperforms existing methods in the literature, the user has to carefully tune some crucial model parameters. Hence, we propose a more adaptive approach, for which a Bayesian framework is adopted. This approach not only outperforms the proposed supervised approach and existing methods in the literature but also provides computation time that competes with optimization-based methods

Application of regularized Richardson–Lucy algorithm for deconvolution of confocal microscopy images

Although confocal microscopes have considerably smaller contribution of out-of-focus light than widefield microscopes, the confocal images can still be enhanced mathematically if the optical and data acquisition effects are accounted for. For that, several deconvolution algorithms have been proposed. As a practical solution, maximum-likelihood algorithms with regularization have been used. However, the choice of regularization parameters is often unknown although it has considerable effect on the result of deconvolution process. The aims of this work were: to find good estimates of deconvolution parameters; and to develop an open source software package that would allow testing different deconvolution algorithms and that would be easy to use in practice. Here, Richardson–Lucy algorithm has been implemented together with the total variation regularization in an open source software package IOCBio Microscope. The influence of total variation regularization on deconvolution process is determined by one parameter. We derived a formula to estimate this regularization parameter automatically from the images as the algorithm progresses. To assess the effectiveness of this algorithm, synthetic images were composed on the basis of confocal images of rat cardiomyocytes. From the analysis of deconvolved results, we have determined under which conditions our estimation of total variation regularization parameter gives good results. The estimated total variation regularization parameter can be monitored during deconvolution process and used as a stopping criterion. An inverse relation between the optimal regularization parameter and the peak signal-to-noise ratio of an image is shown. Finally, we demonstrate the use of the developed software by deconvolving images of rat cardiomyocytes with stained mitochondria and sarcolemma obtained by confocal and widefield microscopes

Blockwise SVD with error in the operator and application to blind deconvolution

We consider linear inverse problems in a nonparametric statistical framework. Both the signal and the operator are unknown and subject to error measurements. We establish minimax rates of convergence under squared error loss when the operator admits a blockwise singular value decomposition (blockwise SVD) and the smoothness of the signal is measured in a Sobolev sense. We construct a nonlinear procedure adapting simultaneously to the unknown smoothness of both the signal and the operator and achieving the optimal rate of convergence to within logarithmic terms. When the noise level in the operator is dominant, by taking full advantage of the blockwise SVD property, we demonstrate that the block SVD procedure overperforms classical methods based on Galerkin projection or nonlinear wavelet thresholding. We subsequently apply our abstract framework to the specific case of blind deconvolution on the torus and on the sphere

Restoration methods for biomedical images in confocal microscopy

Diese Arbeit stellt neue Loesungen zum Problem Bildrestauration im biomedizinischen Bereich vor. Das Konfokal-Mikroskop ist eine verhaeltnismaessig neue Bildungstechnik, die als Standardwerkzeug in biomedizinischen Studien eingesetzt wird. Diese Technik dient zum Sammeln einer Reihe von 2D Bildern der einzelnen Abschnitte innerhalb eines Probestuecks, um eine 3D Darstellung des Gegenstandes zu erzeugen. Trotz seiner verbesserten Belichtungseigenschaften unterliegen die beobachteten Bilder Stoerungen augrund der begrenzten Groesse der Punktantwort (PSF) und das Poisson-Rauschens. Bildrestaurationstechniken versuchen diese Stoerungen herauszurechnen und das Originalbild zu rekonstruieren. Diese Doktorarbeit beginnt mit der Beschreibung des Konfokal-Mikroskops und den Quellen von Artefakten. Dann werden die vorhandenen Bildwiederherstellungsmethoden vorgestellt und verglichen. Die Arbeit ist in drei Teile gegliedert: Im ersten Teil wird eine neue begrenzte blinde Dekonvolutionsmethode eingefuehrt. Durch eine passende Re-Parametrisierung wird dabei a priori Wissen eingebaut. Fuer die PSF wird ein parametrisches Modell, mit einem begrenzten Satz von Basisunktionen benutzt, um Nicht-Negativitaet, zirkulaaere Symmetrie und Limitierung der Frequenzbandbreite sicher zu stellen. Fuer das Bild stellt die quadratische Re-Parametrisierung die Nicht-Negativitaet sicher. Die Entfaltungsmethode wird anhand von simulierten und realen Konfokal-Mikroskopie Daten ausgewertet. Der Vergleich mit einem nicht-parametrisierten Algorithmus zeigt, dass die vorgeschlagene Methode verbesserte Leistung und schnellere Konvergenz erreicht. Im zweiten Teil der Arbeit wird eine neue Methode eingefuehrt, die versucht die anisotrope tiefabhaengige Unschaerfe zu beheben. Wenn roehrenfoermige Gegenstaende -wie Neuronen- abgebildet werden, sind die aufgenommenen Bilder degradiert und die Extraktion der genauen Morphologie der Neuronen wird erschwert. Es wird eine neue Methode vorgeschlagen, mit der sich die PSF ohne irgendein Vorwissen ueber das Belichtungssystem aus dem augenommenen Bild schaetzen laesst. Diese Methode, die auf der Schaetzung des urspruenglichen Gegenstandes basiert ist fuer Faelle verwendbar, in denen der abgebildete Gegenstand eine bekannte Geometrie hat. Mit der vorgeschlagenen Dekonvolutionsmethode werden geometrische Verzerrungen beseitigt und die wiederhergestellten Bilder sind fuer weitere Analysen besser verwendbar. Im dritten Teil wird eine neue Methode zur adaptiven Regularisierung vorgeschlagen. Diese vorgeschlagene Technik passt ihr Verhalten abhaengig von den lokalen Intensitaetsgradient im Bild an. Die neue Technik wird getestet und mit der ''total variation'' und der Tikhonov Regularisierungtechnik verglichen. Die Experimente zeigen, dass mit dem adaptiven Verahren, die Qualitaet der rekonstruierten Bilder verbessert wird.This thesis introduces new solutions to the problem of image restoration in biomedical fields. The confocal microscope is a relatively new imaging technique that is emerging as a standard tool in biomedical studies. This technique is capable of collecting a series of 2D images of single sections inside a specimen to form a 3D image of the object. Despite of its improved imaging properties, the observed images are blurred due to the finite size of the the point spread function and corrupted by Poisson noise due to the counting nature of image detection. Image restoration techniques aim at reversing the degradation and recovering an estimate of the true image. This thesis starts with the description of the confocal microscope and the sources of degradation. Then, the existing image restoration methods are studied and compared. The work done in this thesis is divided into three parts: In the first part, a new constrained blind deconvolution method is introduced. Re-parameterization is used to strictly enforce prior knowledge. A parametric model based on a set of constrained basis functions is used for the PSF to ensure non-negativity, circular symmetry, and band-limitedness. For the image, quadratic re-parameterization ensures non-negativity. The deconvolution method is evaluated on both simulated and real confocal microscopy data sets. The comparison with non-parameteric algorithms shows that the proposed method exhibits improved performance and faster convergence. In the second part, a new method to correct the anisotropic, depth-variant blur is introduced. When objects of tubular-like structure, like neurons, are imaged, the acquired images are degraded and the extraction of accurate morphology of neurons is hampered. A new method to estimate the PSF from the acquired image, without any prior knowledge about the imaging system, is proposed. This method which is based on the estimation of the original object and is suitable for cases in which, the object being imaged has a known geometry. Using the proposed restoration method, geometric distortions are eliminated and the restored images are more suitable for further analysis. In the third part, a new method for adaptive regularization is proposed. The proposed technique adapts its behavior depending on the local activities in the image, as reflected in the magnitude of the intensity gradient. The new technique is tested and compared to both the total variation and the Tikhonov regularization techniques. Experiments show that, using the adaptive technique, the quality of the restored images is improved

3D Architectural Analysis of Neurons, Astrocytes, Vasculature & Nuclei in the Motor and Somatosensory Murine Cortical Columns

Characterization of the complex cortical structure of the brain at a cellular level is a fundamental goal of neuroscience which can provide a better understanding of both normal function as well as disease state progression. Many challenges exist however when carrying out this form of analysis. Immunofluorescent staining is a key technique for revealing 3-dimensional structure, but subsequent fluorescence microscopy is limited by the quantity of simultaneous targets that can be labeled and intrinsic lateral and isotropic axial point-spread function (PSF) blurring during the imaging process in a spectral and depth-dependent manner. Even after successful staining, imaging and optical deconvolution, the sheer density of filamentous processes in the neuropil significantly complicates analysis due to the difficulty of separating individual cells in a highly interconnected network of tightly woven cellular arbors. In order to solve these problems, a variety of methodologies were developed and validated for improved analysis of cortical anatomy. An enhanced immunofluorescent staining and imaging protocol was utilized to precisely locate specific functional regions within brain slices at high magnification and collect four-channel, complete cortical columns. A powerful deconvolution routine was established which collected depth variant PSFs using an optical phantom for image restoration. Fractional volume analysis (FVA) was used to provide preliminary data of the proportions of each stained component in order to statistically characterize the variability within and between the functional regions in a depth-dependent and depth-independent manner. Finally, using machine learning techniques, a supervised learning model was developed that could automatically classify neuronal and astrocytic nuclei within the large cortical column datasets based on perinuclear fluorescence. These annotated nuclei were then used as seed points within their corresponding fluorescent channel for cell individualization in a highly interconnected network. For astrocytes, this technique provides the first method for characterization of complex morphology in an automated fashion over large areas without laborious dye filling or manual tracing