Least Squares Optimal Density Compensation for the Gridding Non-uniform Discrete Fourier Transform

The Gridding algorithm has shown great utility for reconstructing images from non-uniformly spaced samples in the Fourier domain in several imaging modalities. Due to the non-uniform spacing, some correction for the variable density of the samples must be made. Existing methods for generating density compensation values are either sub-optimal or only consider a finite set of points (a set of measure 0) in the optimization. This manuscript presents the first density compensation algorithm for a general trajectory that takes into account the point spread function over a set of non-zero measure. We show that the images reconstructed with Gridding using the density compensation values of this method are of superior quality when compared to density compensation weights determined in other ways. Results are shown with a numerical phantom and with magnetic resonance images of the abdomen and the knee.

RBM-Flow and D-Flow: Invertible Flows with Discrete Energy Base Spaces

Efficient sampling of complex data distributions can be achieved using trained invertible flows (IF), where the model distribution is generated by pushing a simple base distribution through multiple non-linear bijective transformations. However, the iterative nature of the transformations in IFs can limit the approximation to the target distribution. In this paper we seek to mitigate this by implementing RBM-Flow, an IF model whose base distribution is a Restricted Boltzmann Machine (RBM) with a continuous smoothing applied. We show that by using RBM-Flow we are able to improve the quality of samples generated, quantified by the Inception Scores (IS) and Frechet Inception Distance (FID), over baseline models with the same IF transformations, but with less expressive base distributions. Furthermore, we also obtain D-Flow, an IF model with uncorrelated discrete latent variables. We show that D-Flow achieves similar likelihoods and FID/IS scores to those of a typical IF with Gaussian base variables, but with the additional benefit that global features are meaningfully encoded as discrete labels in the latent space.

Slide-free MUSE Microscopy to H&E Histology Modality Conversion via Unpaired Image-to-Image Translation GAN Models

MUSE is a novel slide-free imaging technique for histological examination of tissues that can serve as an alternative to traditional histology. In order to bridge the gap between MUSE and traditional histology, we aim to convert MUSE images to resemble authentic hematoxylin- and eosin-stained (H&E) images. We evaluated four models: a non-machine-learning-based color-mapping unmixing-based tool, CycleGAN, DualGAN, and GANILLA. CycleGAN and GANILLA provided visually compelling results that appropriately transferred H&E style and preserved MUSE content. Based on training an automated critic on real and generated H&E images, we determined that CycleGAN demonstrated the best performance. We have also found that MUSE color inversion may be a necessary step for accurate modality conversion to H&E. We believe that our MUSE-to-H&E model can help improve adoption of novel slide-free methods by bridging a perceptual gap between MUSE imaging and traditional histology.

Motion Compensated Dynamic MRI Reconstruction with Local Affine Optical Flow Estimation

This paper proposes a novel framework to reconstruct the dynamic magnetic resonance images (DMRI) with motion compensation (MC). Due to the inherent motion effects during DMRI acquisition, reconstruction of DMRI using motion estimation/compensation (ME/MC) has been studied under a compressed sensing (CS) scheme. In this paper, by embedding the intensity-based optical flow (OF) constraint into the traditional CS scheme, we are able to couple the DMRI reconstruction with motion field estimation. The formulated optimization problem is solved by a primal-dual algorithm with linesearch due to its efficiency when dealing with non-differentiable problems. With the estimated motion field, the DMRI reconstruction is refined through MC. By employing the multi-scale coarse-to-fine strategy, we are able to update the variables(temporal image sequences and motion vectors) and to refine the image reconstruction alternately. Moreover, the proposed framework is capable of handling a wide class of prior information (regularizations) for DMRI reconstruction, such as sparsity, low rank and total variation. Experiments on various DMRI data, ranging from in vivo lung to cardiac dataset, validate the reconstruction quality improvement using the proposed scheme in comparison to several state-of-the-art algorithms.