15 research outputs found
The Adwords Problem with Strict Capacity Constraints
We study an online assignment problem where the offline servers have capacities, and the objective is to obtain a maximum-weight assignment of requests that arrive online. The weight of edges incident to any server can be at most the server capacity. Our problem is related to the adwords problem, where the assignment to a server is allowed to exceed its capacity. In many applications, however, server capacities are strict and partially-served requests are of no use, motivating the problem we study.
While no deterministic algorithm can be competitive in general for this problem, we give an algorithm with competitive ratio that depends on the ratio of maximum weight of any edge to the capacity of the server it is incident to. If this ratio is 1/2, our algorithm is tight. Further, we give a randomized algorithm that is 6-competitive in expectation for the general problem. Most previous work on the problem and its variants assumes that the edge weights are much smaller than server capacities. Our guarantee, in contrast, does not require any assumptions about job weights. We also give improved lower bounds for both deterministic and randomized algorithms. For the special case of parallel servers, we show that a load-balancing algorithm is tight and near-optimal
Accelerated Motion Correction with Deep Generative Diffusion Models
Magnetic Resonance Imaging (MRI) is a powerful medical imaging modality, but
unfortunately suffers from long scan times which, aside from increasing
operational costs, can lead to image artifacts due to patient motion. Motion
during the acquisition leads to inconsistencies in measured data that manifest
as blurring and ghosting if unaccounted for in the image reconstruction
process. Various deep learning based reconstruction techniques have been
proposed which decrease scan time by reducing the number of measurements needed
for a high fidelity reconstructed image. Additionally, deep learning has been
used to correct motion using end-to-end techniques. This, however, increases
susceptibility to distribution shifts at test time (sampling pattern, motion
level). In this work we propose a framework for jointly reconstructing highly
sub-sampled MRI data while estimating patient motion using diffusion based
generative models. Our method does not make specific assumptions on the
sampling trajectory or motion pattern at training time and thus can be flexibly
applied to various types of measurement models and patient motion. We
demonstrate our framework on retrospectively accelerated 2D brain MRI corrupted
by rigid motion
Conditional Score-Based Reconstructions for Multi-contrast MRI
Magnetic resonance imaging (MRI) exam protocols consist of multiple
contrast-weighted images of the same anatomy to emphasize different tissue
properties. Due to the long acquisition times required to collect fully sampled
k-space measurements, it is common to only collect a fraction of k-space for
some, or all, of the scans and subsequently solve an inverse problem for each
contrast to recover the desired image from sub-sampled measurements. Recently,
there has been a push to further accelerate MRI exams using data-driven priors,
and generative models in particular, to regularize the ill-posed inverse
problem of image reconstruction. These methods have shown promising
improvements over classical methods. However, many of the approaches neglect
the multi-contrast nature of clinical MRI exams and treat each scan as an
independent reconstruction. In this work we show that by learning a joint
Bayesian prior over multi-contrast data with a score-based generative model we
are able to leverage the underlying structure between multi-contrast images and
thus improve image reconstruction fidelity over generative models that only
reconstruct images of a single contrast