abstract: In this work, I present a Bayesian inference computational framework for the analysis of widefield microscopy data that addresses three challenges: (1) counting and localizing stationary fluorescent molecules; (2) inferring a spatially-dependent effective fluorescence profile that describes the spatially-varying rate at which fluorescent molecules emit subsequently-detected photons (due to different illumination intensities or different local environments); and (3) inferring the camera gain. My general theoretical framework utilizes the Bayesian nonparametric Gaussian and beta-Bernoulli processes with a Markov chain Monte Carlo sampling scheme, which I further specify and implement for Total Internal Reflection Fluorescence (TIRF) microscopy data, benchmarking the method on synthetic data. These three frameworks are self-contained, and can be used concurrently so that the fluorescence profile and emitter locations are both considered unknown and, under some conditions, learned simultaneously. The framework I present is flexible and may be adapted to accommodate the inference of other parameters, such as emission photophysical kinetics and the trajectories of moving molecules. My TIRF-specific implementation may find use in the study of structures on cell membranes, or in studying local sample properties that affect fluorescent molecule photon emission rates. / Dissertation/Thesis / Masters Thesis Applied Mathematics 2019

Video compression aims to reduce video file size without impacting visual quality. Existing algorithms mostly use transform coders to convert information from the spatial to frequency domain, and attenuate or remove high frequency components from the sequence. This enables the omission of a large proportion of high frequency information with no discernible visual impact. Sprite-based compression encodes large portions of a scene as a single object in the video sequence, recreating the object in subsequent frames by warping or morphing the sprite to mimic changes in subsequent frames. This thesis sought to improve several aspects of existing sprite based compression approaches, employing a temporal motion model using a low order polynomial to represent the motion of an object across multiple frames in a single model rather than a series of models. The main outcome is the demonstration that motion models used by sprite based video compression can be extended to a full three dimensional model, reducing the overall size of the model, and improving the quality of the sequence at low bit rates. A second outcome is the demonstration that super-resolution processing is not necessary if lanczos spatial interpolation is used instead of bilinear or bi-cubic interpolation, resulting in a savings in computational time and resources. A third outcome is the introduction of a new blending model used to generate image mosaics that improves the quality of the synthesised sequence when zoom is present in the sequence for a given bit-rate. A final outcome is demonstrating that performing superresolution processing and sub-sampling back to the original resolution prior to compression provides benefits in some circumstances.

Resolution is the most important criterion for the clarity of details on an image. Therefore, high resolution images are required in numerous areas. However, obtaining high resolution images has an evident technological cost and the value of these costs change with the quality of used optical systems. Image processing methods are used to obtain high resolution images with low costs. This kind of image improvement is named as superresolution image reconstruction. This thesis focuses on two main titles, one of which is the identification methods of blur parameters, one of the degradation operators, and the stochastic SR image reconstruction methods. The performances of different stochastic SR image reconstruction methods and blur identification methods are shown and compared. Then the identified blur parameters are used in superresolution algorithms and the results are shown.

Miniature cameras play a key role in numerous imaging applications ranging from endoscopy and metrology inspection devices to smartphones and head-mount acquisition systems. However, due to the physical constraints, the imaging conditions, and the low quality of small optics, their imaging capabilities are limited in terms of the delivered resolution, the acquired depth of field, and the captured dynamic range. Computational imaging jointly addresses the imaging system and the reconstructing algorithms to bypass the traditional limits of optical systems and deliver better restorations for various applications. The scene is encoded into a set of efficient measurements which could then be computationally decoded to output a richer estimate of the scene as compared with the raw images captured by conventional imagers. In this dissertation, three task-based computational imaging techniques are developed to make low-quality miniature cameras capable of delivering realistic high-resolution reconstructions, providing full-focus imaging, and acquiring depth information for high dynamic range objects. For the superresolution task, a non-regularized direct superresolution algorithm is developed to achieve realistic restorations without being penalized by improper assumptions (e.g., optimizers, priors, and regularizers) made in the inverse problem. An adaptive frequency-based filtering scheme is introduced to upper bound the reconstruction errors while still producing more fine details as compared with previous methods under realistic imaging conditions. For the full-focus imaging task, a computational depth-based deconvolution technique is proposed to bring a scene captured by an ordinary fixed-focus camera to a full-focus based on a depth-variant point spread function prior. The ringing artifacts are suppressed on three levels: block tiling to eliminate boundary artifacts, adaptive reference maps to reduce ringing initiated by sharp edges, and block-wise deconvolution or depth-based masking to suppress artifacts initiated by neighboring depth-transition surfaces. Finally for the depth acquisition task, a multi-polarization fringe projection imaging technique is introduced to eliminate saturated points and enhance the fringe contrast by selecting the proper polarized channel measurements. The developed technique can be easily extended to include measurements captured under different exposure times to obtain more accurate shape rendering for very high dynamic range objects.

The understanding of the biological processes at the cellular and subcellular level requires the ability to directly visualize them. Fluorescence microscopy played a key role in biomedical imaging because of its high sensitivity and specificity. However, traditional fluorescence microscopy has a limited resolution due to optical diffraction. In recent years, various approaches have been developed to overcome the diffraction limit. Among these techniques, nonlinear structured illumination microscopy (SIM) has been demonstrated a fast and full field superresolution imaging tool, such as Saturated-SIM and Photoswitching-SIM. In this dissertation, I report a new approach that applies nonlinear structured illumination by combining a uniform excitation field and a patterned stimulated emission depletion (STED) field. The nature of STED effect allows fast switching response, negligible stochastic noise during switching, low shot noise and theoretical unlimited resolution, which predicts STED-SIM to be a better nonlinear SIM. After the algorithm development and the feasibility study by simulation, the STED-SIM microscope was tested on fluorescent beads samples and achieved full field imaging over 1 x 10 micron square at the speed of 2s/frame with 4-fold improved resolution. Our STED-SIM technique has been applied on biological samples and superresolution images with tubulin of U2OS cells and granules of neuron cells have been obtained. In this dissertation, an effort to apply a field enhancement mechanism, surface plasmon resonance (SPR), to nonlinear STED-SIM has been made and around 8 time enhancement on STED quenching effect was achieved. Based on this enhancement on STED, 1D SPR enhanced STED-SIM was built and 50 nm resolution of fluorescence beads sample was achieved. Algorithm improvement is required to achieve full field superresolution imaging with SPR enhanced STED-SIM. The application of nonlinear structured illumination in two photon light-sheet microscopy is also studied in this dissertation. Fluorescent cellular imaging of deep internal organs is highly challenging because of the tissue scattering. By combining two photon Bessel beam light-sheet microscopy and nonlinear SIM, 3D live sample imaging at cellular resolution in depth beyond 200 microns has been achieved on live zebrafish. Two-color imaging of pronephric glomeruli and vasculature of zebrafish kidney, whose cellular structures located at the center of the fish body are revealed in high clarity.

For many digital image/video processing applications increasing the spatial resolution is highly beneficial. At higher resolution, TV pictures look more natural and pleasing to the eye, computer vision tasks such as object detection and tracking can be performed with higher precision, medical diagnoses can be made with a higher confidence, security cameras can offer better identification, and satellite imagery can be interpreted with higher accuracy. As such, spatial resolution is an influential parameter in many mainstream imaging applications, and resolution enhancement task naturally arises as a means of increasing the effectiveness of any imaging system used in the mentioned applications. In this thesis, we concentrate on two enhancement problems of practical importance, namely, low-complexity resolution enhancement for customer grade flat panel televisions, and resolution enhancement of noisy high-dimensional hyperspectral imagery. For TV resolution enhancement our main concern is keeping computational complexity at a minimum. The hardware limitations of average customer grade televisions effectively rule out a multi-frame approach. Hence, we take a low-complexity single-frame approach based on exploiting natural image characteristics. For hyperspectral imagery we take advantage of multiple observations in a modified superresolution framework. Here the main challenges are the high dimensionality of hyperspectral data and the noise present in all spectral bands. We design a physical model of the hyperspectral image acquisition process, and based on this model we formulate an iterative resolution enhancement algorithm.

L'imagerie médicale échographique présente plusieurs avantages comme son innocuité, sa facilité d'emploi, la diversité des organes concernés et le faible coût de ce mode d'imagerie. Cependant les images obtenues par échographique souffrent d'une résolution plutôt faible comparées à celle que l'on peut obtenir avec un appareil d'IRM ou en utilisant des rayons X. Le défi majeur de l'échographie médicale est donc de réussir à produire des images avec une résolution beaucoup plus fine, à fréquence nominale fixe.Des travaux ont été entrepris dans ce sens depuis longtemps. Plusieurs pistes ont été explorées. La majorité des travaux effectués jusqu'à présent a consisté à travailler sur l'échographe et particulièrement sur les sondes ultrasonores, avec principalement pour objectif d'augmenter la fréquence des ultrasons utilisés. Cette approche a conduit à l'existence de l'échographie haute résolution, avec cependant une limite importante qui est celle de la profondeur d'exploration.Une autre approche consiste à traiter numériquement des images échographiques classiques pour améliorer leur résolution. Cette méthode a plusieurs avantages, elle permet notamment de contourner la difficulté causée par la réduction de profondeur de champ liée à l'augmentation de la fréquence ultrasonore.Dans cette thèse, nous présentons une méthode permettant d'améliorer la résolution des images échographiques. Le travail de thèse à consister à adapter cette méthode à l'imagerie échographique et à proposer une estimation de la résolution théorique maximale atteinte par cette méthode en fonction de paramètres de l'image dont le SNR, et la largeur de bande de la PSF. Nous avons également proposé une méthode de superrésolution adaptée aux ultrasons. Par son apport sur l'amélioration théorique de la superrésolution et par l'adaptation au cas particulier de l'imagerie ultrasonore, ce travail de thèse ouvre des perspectives sur l'amélioration de la résolution des images échographiques par traitement du signal et de l'image. / Medical Imaging Ultrasound has several advantages such as its safety, ease of use, the diversity of organs that can be imaged and the low cost of this imaging mode. However, the images obtained by ultrasound suffer from relatively low resolution compared to others than can be obtain with an MRI or using X-rays. The major challenge of medical ultrasound is the ability to produce images with a resolution much finer, without modifying the nominal frequency.Work has been undertaken in this direction for some time. Several approaches have been explored. Most of the work done so far has been to work on the ultrasound acquiring device and particularly on ultrasonic probes, with main objective to increase the frequency of ultrasound used. This approach has led to the existence of high-resolution ultrasound, but with the reduction of the depth of exploration as an important limitation.Another approach is to treat numerically conventional ultrasound images to improve resolution. This method has several advantages, it allows to circumvent such difficulties caused by the reduction of depth of field due to the increase in the ultrasonic frequency.In this thesis, we present a method to improve the resolution of ultrasound images. The thesis to be to adapt this method to ultrasound imaging and to provide an estimate of the maximum theoretical resolution achieved by this method based on image parameters including SNR and the bandwidth of the PSF. We also proposed a method of superresolution suitable for ultrasound. By providing on improving theoretical superresolution and adaptation to the particular case of ultrasound, this thesis opens up on improving the resolution of ultrasound images by processing the signal and the image.

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