RED-PSM: Regularization by Denoising of Partially Separable Models for Dynamic Imaging

Dynamic imaging addresses the recovery of a time-varying 2D or 3D object at each time instant using its undersampled measurements. In particular, in the case of dynamic tomography, only a single projection at a single view angle may be available at a time, making the problem severely ill-posed. In this work, we propose an approach, RED-PSM, which combines for the first time two powerful techniques to address this challenging imaging problem. The first, are partially separable models, which have been used to efficiently introduce a low-rank prior for the spatio-temporal object. The second is the recent Regularization by Denoising (RED), which provides a flexible framework to exploit the impressive performance of state-of-the-art image denoising algorithms, for various inverse problems. We propose a partially separable objective with RED and an optimization scheme with variable splitting and ADMM, and prove convergence of our objective to a value corresponding to a stationary point satisfying the first order optimality conditions. Convergence is accelerated by a particular projection-domain-based initialization. We demonstrate the performance and computational improvements of our proposed RED-PSM with a learned image denoiser by comparing it to a recent deep-prior-based method TD-DIP.

Improving Dense Contrastive Learning with Dense Negative Pairs

Many contrastive representation learning methods learn a single global representation of an entire image. However, dense contrastive representation learning methods such as DenseCL [19] can learn better representations for tasks requiring stronger spatial localization of features, such as multi-label classification, detection, and segmentation. In this work, we study how to improve the quality of the representations learned by DenseCL by modifying the training scheme and objective function, and propose DenseCL++. We also conduct several ablation studies to better understand the effects of: (i) various techniques to form dense negative pairs among augmentations of different images, (ii) cross-view dense negative and positive pairs, and (iii) an auxiliary reconstruction task. Our results show 3.5% and 4% mAP improvement over SimCLR [3] and DenseCL in COCO multi-label classification. In COCO and VOC segmentation tasks, we achieve 1.8% and 0.7% mIoU improvements over SimCLR, respectively.

Dynamic Tomography Reconstruction by Projection-Domain Separable Modeling

In dynamic tomography the object undergoes changes while projections are being acquired sequentially in time. The resulting inconsistent set of projections cannot be used directly to reconstruct an object corresponding to a time instant. Instead, the objective is to reconstruct a spatio-temporal representation of the object, which can be displayed as a movie. We analyze conditions for unique and stable solution of this ill-posed inverse problem, and present a recovery algorithm, validating it experimentally. We compare our approach to one based on the recently proposed GMLR variation on deep prior for video, demonstrating the advantages of the proposed approach.

Scatter Correction in X-ray CT by Physics-Inspired Deep Learning

A fundamental problem in X-ray Computed Tomography (CT) is the scatter due to interaction of photons with the imaged object. Unless corrected, scatter manifests itself as degradations in the reconstructions in the form of various artifacts. Scatter correction is therefore critical for reconstruction quality. Scatter correction methods can be divided into two categories: hardware-based; and software-based. Despite success in specific settings, hardware-based methods require modification in the hardware, or increase in the scan time or dose. This makes software-based methods attractive. In this context, Monte-Carlo based scatter estimation, analytical-numerical, and kernel-based methods were developed. Furthermore, data-driven approaches to tackle this problem were recently demonstrated. In this work, two novel physics-inspired deep-learning-based methods, PhILSCAT and OV-PhILSCAT, are proposed. The methods estimate and correct for the scatter in the acquired projection measurements. They incorporate both an initial reconstruction of the object of interest and the scatter-corrupted measurements related to it. They use a common deep neural network architecture and cost function, both tailored to the problem. Numerical experiments with data obtained by Monte-Carlo simulations of the imaging of phantoms reveal significant improvement over a recent purely projection-domain deep neural network scatter correction method.