Accelerated gradient methods for total-variation-based CT image reconstruction

Total-variation (TV)-based Computed Tomography (CT) image reconstruction has shown experimentally to be capable of producing accurate reconstructions from sparse-view data. In particular TV-based reconstruction is very well suited for images with piecewise nearly constant regions. Computationally, however, TV-based reconstruction is much more demanding, especially for 3D imaging, and the reconstruction from clinical data sets is far from being close to real-time. This is undesirable from a clinical perspective, and thus there is an incentive to accelerate the solution of the underlying optimization problem. The TV reconstruction can in principle be found by any optimization method, but in practice the large-scale systems arising in CT image reconstruction preclude the use of memory-demanding methods such as Newton's method. The simple gradient method has much lower memory requirements, but exhibits slow convergence. In the present work we consider the use of two accelerated gradient-based methods, GPBB and UPN, for reducing the number of gradient method iterations needed to achieve a high-accuracy TV solution in CT image reconstruction. The former incorporates several heuristics from the optimization literature such as Barzilai-Borwein (BB) step size selection and nonmonotone line search. The latter uses a cleverly chosen sequence of auxiliary points to achieve a better convergence rate. The methods are memory efficient and equipped with a stopping criterion to ensure that the TV reconstruction has indeed been found. An implementation of the methods (in C with interface to Matlab) is available for download from http://www2.imm.dtu.dk/~pch/TVReg/. We compare the proposed methods with the standard gradient method, applied to a 3D test problem with synthetic few-view data. We find experimentally that for realistic parameters the proposed methods significantly outperform the gradient method.Comment: 4 pages, 2 figure

Large-Scale Automatic Reconstruction of Neuronal Processes from Electron Microscopy Images

Automated sample preparation and electron microscopy enables acquisition of very large image data sets. These technical advances are of special importance to the field of neuroanatomy, as 3D reconstructions of neuronal processes at the nm scale can provide new insight into the fine grained structure of the brain. Segmentation of large-scale electron microscopy data is the main bottleneck in the analysis of these data sets. In this paper we present a pipeline that provides state-of-the art reconstruction performance while scaling to data sets in the GB-TB range. First, we train a random forest classifier on interactive sparse user annotations. The classifier output is combined with an anisotropic smoothing prior in a Conditional Random Field framework to generate multiple segmentation hypotheses per image. These segmentations are then combined into geometrically consistent 3D objects by segmentation fusion. We provide qualitative and quantitative evaluation of the automatic segmentation and demonstrate large-scale 3D reconstructions of neuronal processes from a $\mathbf{27,000}$ $\mathbf{\mu m^3}$ volume of brain tissue over a cube of $\mathbf{30 \; \mu m}$ in each dimension corresponding to 1000 consecutive image sections. We also introduce Mojo, a proofreading tool including semi-automated correction of merge errors based on sparse user scribbles

Probabilistic 3D surface reconstruction from sparse MRI information

Surface reconstruction from magnetic resonance (MR) imaging data is indispensable in medical image analysis and clinical research. A reliable and effective reconstruction tool should: be fast in prediction of accurate well localised and high resolution models, evaluate prediction uncertainty, work with as little input data as possible. Current deep learning state of the art (SOTA) 3D reconstruction methods, however, often only produce shapes of limited variability positioned in a canonical position or lack uncertainty evaluation. In this paper, we present a novel probabilistic deep learning approach for concurrent 3D surface reconstruction from sparse 2D MR image data and aleatoric uncertainty prediction. Our method is capable of reconstructing large surface meshes from three quasi-orthogonal MR imaging slices from limited training sets whilst modelling the location of each mesh vertex through a Gaussian distribution. Prior shape information is encoded using a built-in linear principal component analysis (PCA) model. Extensive experiments on cardiac MR data show that our probabilistic approach successfully assesses prediction uncertainty while at the same time qualitatively and quantitatively outperforms SOTA methods in shape prediction. Compared to SOTA, we are capable of properly localising and orientating the prediction via the use of a spatially aware neural network.Comment: MICCAI 202

Scalable Dense Monocular Surface Reconstruction

This paper reports on a novel template-free monocular non-rigid surface reconstruction approach. Existing techniques using motion and deformation cues rely on multiple prior assumptions, are often computationally expensive and do not perform equally well across the variety of data sets. In contrast, the proposed Scalable Monocular Surface Reconstruction (SMSR) combines strengths of several algorithms, i.e., it is scalable with the number of points, can handle sparse and dense settings as well as different types of motions and deformations. We estimate camera pose by singular value thresholding and proximal gradient. Our formulation adopts alternating direction method of multipliers which converges in linear time for large point track matrices. In the proposed SMSR, trajectory space constraints are integrated by smoothing of the measurement matrix. In the extensive experiments, SMSR is demonstrated to consistently achieve state-of-the-art accuracy on a wide variety of data sets.Comment: International Conference on 3D Vision (3DV), Qingdao, China, October 201

DeformNet: Free-Form Deformation Network for 3D Shape Reconstruction from a Single Image

3D reconstruction from a single image is a key problem in multiple applications ranging from robotic manipulation to augmented reality. Prior methods have tackled this problem through generative models which predict 3D reconstructions as voxels or point clouds. However, these methods can be computationally expensive and miss fine details. We introduce a new differentiable layer for 3D data deformation and use it in DeformNet to learn a model for 3D reconstruction-through-deformation. DeformNet takes an image input, searches the nearest shape template from a database, and deforms the template to match the query image. We evaluate our approach on the ShapeNet dataset and show that - (a) the Free-Form Deformation layer is a powerful new building block for Deep Learning models that manipulate 3D data (b) DeformNet uses this FFD layer combined with shape retrieval for smooth and detail-preserving 3D reconstruction of qualitatively plausible point clouds with respect to a single query image (c) compared to other state-of-the-art 3D reconstruction methods, DeformNet quantitatively matches or outperforms their benchmarks by significant margins. For more information, visit: https://deformnet-site.github.io/DeformNet-website/ .Comment: 11 pages, 9 figures, NIP