In this work, we propose a learning-based variational network (VN) approach for reconstruction of low-dose 3D computed tomography data. We focus on two methods to decrease the radiation dose: (1) x-ray tube current reduction, which reduces the signal-to-noise ratio, and (2) x-ray beam interruption, which undersamples data and results in images with aliasing artifacts. While the learned VN denoises the current-reduced images in the first case, it reconstructs the undersampled data in the second case. Different VNs for denoising and reconstruction are trained on a single clinical 3D abdominal data set. The VNs are compared against state-of-the-art model-based denoising and sparse reconstruction techniques on a different clinical abdominal 3D data set with 4-fold dose reduction. Our results suggest that the proposed VNs enable higher radiation dose reductions and/or increase the image quality for a given dose.

Robust principal component analysis (RPCA) via decomposition into low-rank plus sparse matrices offers a powerful framework for a large variety of applications such as image processing, video processing, and 3-D computer vision. Indeed, most of the time these applications require to detect sparse outliers from the observed imagery data that can be approximated by a low-rank matrix. Moreover, most of the time experiments show that RPCA with additional spatial and/or temporal constraints often outperforms the state-of-the-art algorithms in these applications. Thus, the aim of this paper is to survey the applications of RPCA in computer vision. In the first part of this paper, we review representative image processing applications as follows: 1) low-level imaging such as image recovery and denoising, image composition, image colorization, image alignment and rectification, multifocus image, and face recognition; 2) medical imaging such as dynamic magnetic resonance imaging (MRI) for acceleration of data acquisition, background suppression, and learning of interframe motion fields; and 3) imaging for 3-D computer vision with additional depth information such as in structure from motion (SfM) and 3-D motion recovery. In the second part, we present the applications of RPCA in video processing which utilize additional spatial and temporal information compared to image processing. Specifically, we investigate video denoising and restoration, hyperspectral video, and background/foreground separation. Finally, we provide perspectives on possible future research directions and algorithmic frameworks that are suitable for these applications.

While current state of the art MR-PET scanners enable simultaneous MR and PET measurements, the acquired data sets are still usually reconstructed separately. We propose a new multi-modality reconstruction framework using second order Total Generalized Variation (TGV) as a dedicated multi-channel regularization functional that jointly reconstructs images from both modalities. In this way, information about the underlying anatomy is shared during the image reconstruction process while unique differences are preserved. Results from numerical simulations and in-vivo experiments using a range of accelerated MR acquisitions and different MR image contrasts demonstrate improved PET image quality, resolution, and quantitative accuracy.

Imaging of cardiac perfusion with MR is a challenging area of research especially due to the motion of the heart and limited time of data acquisition. Compressed sensing is a popular signal estimation method recently adopted by researchers in MRI which can improve the spatial and/or temporal resolution of the acquired images by reducing the number of necessary samples for image reconstruction. This paper focuses on performance of temporal regularization with total variation and wavelets in compressed sensing. The impact of the choice of regularization parameters on the image quality and the temporal variation of intensity in region of interests (ROIs) are discussed. It is found that selecting the regularization parameter so as to optimize the quality of the reconstructed image sequence as a whole, leads to erroneous reconstruction of certain regions due to over regularization.

Parallel MRI reconstruction is formulated as a superresolution problem using coil sensitivities acquired with higher spatial resolution than the actual image. Array coils with a large number of small elements that present very localized and highly modulated sensitivity functions will form an encoding basis to estimate high k-space components from limited k-space acquisitions. The method is proposed for spatial resolution enhancement of intrinsic low-resolution modalities such as spectroscopic imaging and functional MRI where the coil sensitivities are varying withing the image voxel.