Phase-Retrieved Tomography enables imaging of a Tumor Spheroid in Mesoscopy Regime

Optical tomographic imaging of biological specimen bases its reliability on the combination of both accurate experimental measures and advanced computational techniques. In general, due to high scattering and absorption in most of the tissues, multi view geometries are required to reduce diffuse halo and blurring in the reconstructions. Scanning processes are used to acquire the data but they inevitably introduces perturbation, negating the assumption of aligned measures. Here we propose an innovative, registration free, imaging protocol implemented to image a human tumor spheroid at mesoscopic regime. The technique relies on the calculation of autocorrelation sinogram and object autocorrelation, finalizing the tomographic reconstruction via a three dimensional Gerchberg Saxton algorithm that retrieves the missing phase information. Our method is conceptually simple and focuses on single image acquisition, regardless of the specimen position in the camera plane. We demonstrate increased deep resolution abilities, not achievable with the current approaches, rendering the data alignment process obsolete.Comment: 21 pages, 5 figure

Inversion and Symmetries of the Star Transform

The star transform is a generalized Radon transform mapping a function of two variables to its integrals along "star-shaped" trajectories, which consist of a finite number of rays emanating from a common vertex. Such operators appear in mathematical models of various imaging modalities based on scattering of elementary particles. The paper presents a comprehensive study of the inversion of the star transform. We describe the necessary and sufficient conditions for invertibility of the star transform, introduce a new inversion formula and discuss its stability properties. As an unexpected bonus of our approach, we prove a conjecture from algebraic geometry about the zero sets of elementary symmetric polynomials

Task adapted reconstruction for inverse problems

The paper considers the problem of performing a task defined on a model parameter that is only observed indirectly through noisy data in an ill-posed inverse problem. A key aspect is to formalize the steps of reconstruction and task as appropriate estimators (non-randomized decision rules) in statistical estimation problems. The implementation makes use of (deep) neural networks to provide a differentiable parametrization of the family of estimators for both steps. These networks are combined and jointly trained against suitable supervised training data in order to minimize a joint differentiable loss function, resulting in an end-to-end task adapted reconstruction method. The suggested framework is generic, yet adaptable, with a plug-and-play structure for adjusting both the inverse problem and the task at hand. More precisely, the data model (forward operator and statistical model of the noise) associated with the inverse problem is exchangeable, e.g., by using neural network architecture given by a learned iterative method. Furthermore, any task that is encodable as a trainable neural network can be used. The approach is demonstrated on joint tomographic image reconstruction, classification and joint tomographic image reconstruction segmentation

Reduced and coded sensing methods for x-ray based security

Current x-ray technologies provide security personnel with non-invasive sub-surface imaging and contraband detection in various portal screening applications such as checked and carry-on baggage as well as cargo. Computed tomography (CT) scanners generate detailed 3D imagery in checked bags; however, these scanners often require significant power, cost, and space. These tomography machines are impractical for many applications where space and power are often limited such as checkpoint areas. Reducing the amount of data acquired would help reduce the physical demands of these systems. Unfortunately this leads to the formation of artifacts in various applications, thus presenting significant challenges in reconstruction and classification. As a result, the goal is to maintain a certain level of image quality but reduce the amount of data gathered. For the security domain this would allow for faster and cheaper screening in existing systems or allow for previously infeasible screening options due to other operational constraints. While our focus is predominantly on security applications, many of the techniques can be extended to other fields such as the medical domain where a reduction of dose can allow for safer and more frequent examinations. This dissertation aims to advance data reduction algorithms for security motivated x-ray imaging in three main areas: (i) development of a sensing aware dimensionality reduction framework, (ii) creation of linear motion tomographic method of object scanning and associated reconstruction algorithms for carry-on baggage screening, and (iii) the application of coded aperture techniques to improve and extend imaging performance of nuclear resonance fluorescence in cargo screening. The sensing aware dimensionality reduction framework extends existing dimensionality reduction methods to include knowledge of an underlying sensing mechanism of a latent variable. This method provides an improved classification rate over classical methods on both a synthetic case and a popular face classification dataset. The linear tomographic method is based on non-rotational scanning of baggage moved by a conveyor belt, and can thus be simpler, smaller, and more reliable than existing rotational tomography systems at the expense of more challenging image formation problems that require special model-based methods. The reconstructions for this approach are comparable to existing tomographic systems. Finally our coded aperture extension of existing nuclear resonance fluorescence cargo scanning provides improved observation signal-to-noise ratios. We analyze, discuss, and demonstrate the strengths and challenges of using coded aperture techniques in this application and provide guidance on regimes where these methods can yield gains over conventional methods