Blind Deblurring Reconstruction Technique with Applications in PET Imaging

We developed an empirical PET model taking into account system blurring and a blind iterative reconstruction scheme that estimates both the actual image and the point spread function of the system. Reconstruction images of high quality can be acquired by using the proposed reconstruction technique for both synthetic and experimental data. In the synthetic data study, the algorithm reduces image blurring and preserves the edges without introducing extra artifacts. The localized measurement shows that the performance of the reconstruction image improved by up to 100%. In experimental data studies, the contrast and quality of reconstruction is substantially improved. The proposed method shows promise in tumor localization and quantification

ParaPET: non-invasive deep learning method for direct parametric brain PET reconstruction using histoimages.

BACKGROUND The indirect method for generating parametric images in positron emission tomography (PET) involves the acquisition and reconstruction of dynamic images and temporal modelling of tissue activity given a measured arterial input function. This approach is not robust, as noise in each dynamic image leads to a degradation in parameter estimation. Direct methods incorporate into the image reconstruction step both the kinetic and noise models, leading to improved parametric images. These methods require extensive computational time and large computing resources. Machine learning methods have demonstrated significant potential in overcoming these challenges. But they are limited by the requirement of a paired training dataset. A further challenge within the existing framework is the use of state-of-the-art arterial input function estimation via temporal arterial blood sampling, which is an invasive procedure, or an additional magnetic resonance imaging (MRI) scan for selecting a region where arterial blood signal can be measured from the PET image. We propose a novel machine learning approach for reconstructing high-quality parametric brain images from histoimages produced from time-of-flight PET data without requiring invasive arterial sampling, an MRI scan, or paired training data from standard field-of-view scanners. RESULT The proposed is tested on a simulated phantom and five oncological subjects undergoing an 18F-FDG-PET scan of the brain using Siemens Biograph Vision Quadra. Kinetic parameters set in the brain phantom correlated strongly with the estimated parameters (K1, k2 and k3, Pearson correlation coefficient of 0.91, 0.92 and 0.93) and a mean squared error of less than 0.0004. In addition, our method significantly outperforms (p < 0.05, paired t-test) the conventional nonlinear least squares method in terms of contrast-to-noise ratio. At last, the proposed method was found to be 37% faster than the conventional method. CONCLUSION We proposed a direct non-invasive DL-based reconstruction method and produced high-quality parametric maps of the brain. The use of histoimages holds promising potential for enhancing the estimation of parametric images, an area that has not been extensively explored thus far. The proposed method can be applied to subject-specific dynamic PET data alone

First order algorithms in variational image processing

Variational methods in imaging are nowadays developing towards a quite universal and flexible tool, allowing for highly successful approaches on tasks like denoising, deblurring, inpainting, segmentation, super-resolution, disparity, and optical flow estimation. The overall structure of such approaches is of the form ${\cal D}(Ku) + \alpha {\cal R} (u) \rightarrow \min_u$ ; where the functional ${\cal D}$ is a data fidelity term also depending on some input data $f$ and measuring the deviation of $Ku$ from such and ${\cal R}$ is a regularization functional. Moreover $K$ is a (often linear) forward operator modeling the dependence of data on an underlying image, and $\alpha$ is a positive regularization parameter. While ${\cal D}$ is often smooth and (strictly) convex, the current practice almost exclusively uses nonsmooth regularization functionals. The majority of successful techniques is using nonsmooth and convex functionals like the total variation and generalizations thereof or $\ell_1$-norms of coefficients arising from scalar products with some frame system. The efficient solution of such variational problems in imaging demands for appropriate algorithms. Taking into account the specific structure as a sum of two very different terms to be minimized, splitting algorithms are a quite canonical choice. Consequently this field has revived the interest in techniques like operator splittings or augmented Lagrangians. Here we shall provide an overview of methods currently developed and recent results as well as some computational studies providing a comparison of different methods and also illustrating their success in applications.Comment: 60 pages, 33 figure

Training Implicit Networks for Image Deblurring using Jacobian-Free Backpropagation

Recent efforts in applying implicit networks to solve inverse problems in imaging have achieved competitive or even superior results when compared to feedforward networks. These implicit networks only require constant memory during backpropagation, regardless of the number of layers. However, they are not necessarily easy to train. Gradient calculations are computationally expensive because they require backpropagating through a fixed point. In particular, this process requires solving a large linear system whose size is determined by the number of features in the fixed point iteration. This paper explores a recently proposed method, Jacobian-free Backpropagation (JFB), a backpropagation scheme that circumvents such calculation, in the context of image deblurring problems. Our results show that JFB is comparable against fine-tuned optimization schemes, state-of-the-art (SOTA) feedforward networks, and existing implicit networks at a reduced computational cost

A Deconvolution Framework with Applications in Medical and Biological Imaging

A deconvolution framework is presented in this thesis and applied to several problems in medical and biological imaging. The framework is designed to contain state of the art deconvolution methods, to be easily expandable and to combine different components arbitrarily. Deconvolution is an inverse problem and in order to cope with its ill-posed nature, suitable regularization techniques and additional restrictions are required. A main objective of deconvolution methods is to restore degraded images acquired by fluorescence microscopy which has become an important tool in biological and medical sciences. Fluorescence microscopy images are degraded by out-of-focus blurring and noise and the deconvolution algorithms to restore these images are usually called deblurring methods. Many deblurring methods were proposed to restore these images in the last decade which are part of the deconvolution framework. In addition, existing deblurring techniques are improved and new components for the deconvolution framework are developed. A considerable improvement could be obtained by combining a state of the art regularization technique with an additional non-negativity constraint. A real biological screen analysing a specific protein in human cells is presented and shows the need to analyse structural information of fluorescence images. Such an analysis requires a good image quality which is the aim of the deblurring methods if the required image quality is not given. For a reliable understanding of cells and cellular processes, high resolution 3D images of the investigated cells are necessary. However, the ability of fluorescence microscopes to image a cell in 3D is limited since the resolution along the optical axis is by a factor of three worse than the transversal resolution. Standard microscopy image deblurring techniques are able to improve the resolution but the problem of a lower resolution in direction along the optical axis remains. It is however possible to overcome this problem using Axial Tomography providing tilted views of the object by rotating it under the microscope. The rotated images contain additional information about the objects which can be used to improve the resolution along the optical axis. In this thesis, a sophisticated method to reconstruct a high resolution Axial Tomography image on basis of the developed deblurring methods is presented. The deconvolution methods are also used to reconstruct the dose distribution in proton therapy on basis of measured PET images. Positron emitters are activated by proton beams but a PET image is not directly proportional to the delivered radiation dose distribution. A PET signal can be predicted by a convolution of the planned dose with specific filter functions. In this thesis, a dose reconstruction method based on PET images which reverses the convolution approach is presented and the potential to reconstruct the actually delivered dose distribution from measured PET images is investigated. Last but not least, a new denoising method using higher-order statistic information of a given Gaussian noise signal is presented and compared to state of the art denoising methods

The Bubble Box: Towards an Automated Visual Sensor for 3D Analysis and Characterization of Marine Gas Release Sites

Several acoustic and optical techniques have been used for characterizing natural and anthropogenic gas leaks (carbon dioxide, methane) from the ocean floor. Here, single-camera based methods for bubble stream observation have become an important tool, as they help estimating flux and bubble sizes under certain assumptions. However, they record only a projection of a bubble into the camera and therefore cannot capture the full 3D shape, which is particularly important for larger, non-spherical bubbles. The unknown distance of the bubble to the camera (making it appear larger or smaller than expected) as well as refraction at the camera interface introduce extra uncertainties. In this article, we introduce our wide baseline stereo-camera deep-sea sensor bubble box that overcomes these limitations, as it observes bubbles from two orthogonal directions using calibrated cameras. Besides the setup and the hardware of the system, we discuss appropriate calibration and the different automated processing steps deblurring, detection, tracking, and 3D fitting that are crucial to arrive at a 3D ellipsoidal shape and rise speed of each bubble. The obtained values for single bubbles can be aggregated into statistical bubble size distributions or fluxes for extrapolation based on diffusion and dissolution models and large scale acoustic surveys. We demonstrate and evaluate the wide baseline stereo measurement model using a controlled test setup with ground truth information