Eigensensing And Deconvolution For The Reconstruction Of Heat Absorption Profiles From Photoacoustic Tomography Data

Photoacoustic tomography (PAT) is a relatively recent imaging modality that is promising for breast cancer detection and breast screening. It combines the high intrinsic contrast of optical radiation with acoustic imaging at submillimeter spatial resolution through the photoacoustic effect of absorption and thermal expansion. However, image reconstruction from boundary measurements of the propagating wave field is still a challenging inverse problem. Here we propose a new theoretical framework, for which we coin the term eigensensing, to recover the heat absorption profile of the tissue. One of the main features of our method is that there is no explicit forward model that needs to be used within a (usually) slow iterative scheme. Instead, the eigensensing principle allow us to computationally obtain several intermediate images that are blurred by known convolution kernels which are chosen as the eigenfunctions of the spatial Laplace operator. The source image can then be reconstructed by a joint deconvolution algorithm that uses the intermediate images as input. Moreover, total variation regularization is added to make the inverse problem well-posed and to favor piecewise-smooth images.

Reconstruction Methods for Cryo-Electron Microscopy: From Model-based to Data-driven

Laurène Donati

The topic of this thesis is the development of new reconstruction methods for cryo-electron microscopy (cryo-EM). Cryo-EM has revolutionized the field of structural biology over the last decade and now permits the regular discovery of biostructures. Yet, the technical challenges associated to cryo-EM are still numerous, and the measurements remain notoriously difficult to process. This calls for fast and robust algorithms that can reliably handle the challenging reconstruction task at hand. In this thesis, we investigated two reconstruction paradigms: model-based and data-driven. Model-based methods formulate the reconstruction task as an inverse problem and rely on a faithful model of the acquisition physics. By contrast, the central philosophy of data-driven approaches is to let the reconstruction algorithm be guided by the measured data through some learning procedure. Both paradigms share a tight link in all our works: their reliance on a rigorous mathematical formulation of the cryo-EM imaging model. The first cryo-EM method we considered is scanning transmission electron tomography (STET), a modality whose primary concern is to reduce the electron dosage required for accurate imaging. To handle this, we developed a tailored acquisition-reconstruction STET framework that relies on the principles of compressed sensing. This scheme permits high-quality reconstruction from a reduced number of measurements, hence greatly preserving the sample. We then designed several reconstruction algorithms for single-particle analysis (SPA), a popular cryo-EM method that enables the determination of structures at near-atomic resolution. A key challenge for the deployment of robust, iterative reconstruction methods in SPA is that they usually come with a prohibitive computational cost if not carefully engineered. To circumvent this problem, we developed a regularized reconstruction scheme whose cost-dominant operation is recast as a discrete convolution, which makes the use of our robust scheme feasible in SPA. Building on this development, we devised a joint optimization framework that efficiently alternates between the reconstruction and the estimation of the unknown orientations. We then explored a learning-based method to estimate the unknown orientations in SPA directly from the acquired dataset of projections. Capitalizing on our ability to model the cryo-EM procedure, we generated large synthetic SPA datasets to train a function---parametrized as a neural network---to predict the relative orientation between two projections based on their similarity. The framework relies on the postulate that it is possible to recover, from these estimated orientation distances, the orientations themselves through an appropriate minimization scheme, as supported by preliminary tests. Finally, we developed a completely new paradigm for SPA reconstruction that leverages the remarkable capability of deep neural networks to capture data distribution. The proposed algorithm uses a generative adversarial network to learn the 3D structure that has simulated projections that most closely match the real data in a distributional sense. By doing so, it can resolve a 3D structure in a single algorithmic run using only the dataset of projections and CTF estimations as inputs. Hence, it bypasses many processing steps that are necessary in the usual cryo-EM reconstruction pipeline, which opens new perspectives for reconstruction in SPA.

EPFL2020

From Classical to Unsupervised-Deep-Learning Methods for Solving Inverse Problems in Imaging.

Harshit Gupta

In this thesis, we propose new algorithms to solve inverse problems in the context of biomedical images. Due to ill-posedness, solving these problems require some prior knowledge of the statistics of the underlying images. The traditional algorithms, in the field, assume prior knowledge related to smoothness or sparsity of these images. Recently, they have been outperformed by the second generation algorithms which harness the power of neural networks to learn required statistics from training data. Even more recently, last generation deep-learning-based methods have emerged which require neither training nor training data. This thesis devises algorithms which progress through these generations. It extends these generations to novel formulations and applications while bringing more robustness. In parallel, it also progresses in terms of complexity, from proposing algorithms for problems with 1D data and an exact known forward model to the ones with 4D data and an unknown parametric forward model. We introduce five main contributions. The last three of them propose deep-learning-based latest-generation algorithms that require no prior training. 1) We develop algorithms to solve the continuous-domain formulation of inverse problems with both classical Tikhonov and total-variation regularizations. We formalize the problems, characterize the solution set, and devise numerical approaches to find the solutions. 2) We propose an algorithm that improves upon end-to-end neural-network-based second generation algorithms. In our method, a neural network is first trained as a projector on a training set, and is then plugged in as a projector inside the projected gradient descent (PGD). Since the problem is nonconvex, we relax the PGD to ensure convergence to a local minimum under some constraints. This method outperforms all the previous generation algorithms for Computed Tomography (CT). 3) We develop a novel time-dependent deep-image-prior algorithm for modalities that involve a temporal sequence of images. We parameterize them as the output of an untrained neural network fed with a sequence of latent variables. To impose temporal directionality, the latent variables are assumed to lie on a 1D manifold. The network is then tuned to minimize the data fidelity. We obtain state-of-the-art results in dynamic magnetic resonance imaging (MRI) and even recover intra-frame images. 4) We propose a novel reconstruction paradigm for cryo-electron-microscopy (CryoEM) called CryoGAN. Motivated by generative adversarial networks (GANs), we reconstruct a biomolecule's 3D structure such that its CryoEM measurements resemble the acquired data in a distributional sense. The algorithm is pose-or-likelihood-estimation-free, needs no ab initio, and is proven to have a theoretical guarantee of recovery of the true structure. 5) We extend CryoGAN to reconstruct continuously varying conformations of a structure from heterogeneous data. We parameterize the conformations as the output of a neural network fed with latent variables on a low-dimensional manifold. The method is shown to recover continuous protein conformations and their energy landscape.

EPFL2020

Differential Phase-Contrast X-Ray Computed Tomography: From Model Discretization To Image Reconstruction

Masih Nilchian, Michaël Unser

Our contribution in this paper is two fold. First, we propose a novel discretization of the forward model for differential phase-contrast imaging that uses B-spline basis functions. The approach yields a fast and accurate algorithm for implementing the forward model, which is based on the first derivative of the Radon transform. Second, as an alternative to the FBP-like approaches that are currently used in practice, we present an iterative reconstruction algorithm that remains more faithful to the data when the number of projections dwindles. Since the reconstruction is an ill-posed problem, we impose a total-variation (TV) regularization constraint. We propose to solve the reconstruction problem using the alternating direction method of multipliers (ADMM). A specificity of our system is the use of a preconditioner that improves the convergence rate of the linear solver in ADMM. Our experiments on test data suggest that our method can achieve the same quality as the standard direct reconstruction, while using only one-third of the projection data. We also find that the approach is much faster than the standard algorithms (ISTA and FISTA) that are typically used for solving linear inverse problems subject to the TV regularization constraint.

Ieee2012

Reconstruction Methods for Cryo-Electron Microscopy: From Model-based to Data-driven

Laurène Donati

EPFL2020

From Classical to Unsupervised-Deep-Learning Methods for Solving Inverse Problems in Imaging.

Harshit Gupta

EPFL2020