4,876 research outputs found
WARP: Wavelets with adaptive recursive partitioning for multi-dimensional data
Effective identification of asymmetric and local features in images and other
data observed on multi-dimensional grids plays a critical role in a wide range
of applications including biomedical and natural image processing. Moreover,
the ever increasing amount of image data, in terms of both the resolution per
image and the number of images processed per application, requires algorithms
and methods for such applications to be computationally efficient. We develop a
new probabilistic framework for multi-dimensional data to overcome these
challenges through incorporating data adaptivity into discrete wavelet
transforms, thereby allowing them to adapt to the geometric structure of the
data while maintaining the linear computational scalability. By exploiting a
connection between the local directionality of wavelet transforms and recursive
dyadic partitioning on the grid points of the observation, we obtain the
desired adaptivity through adding to the traditional Bayesian wavelet
regression framework an additional layer of Bayesian modeling on the space of
recursive partitions over the grid points. We derive the corresponding
inference recipe in the form of a recursive representation of the exact
posterior, and develop a class of efficient recursive message passing
algorithms for achieving exact Bayesian inference with a computational
complexity linear in the resolution and sample size of the images. While our
framework is applicable to a range of problems including multi-dimensional
signal processing, compression, and structural learning, we illustrate its work
and evaluate its performance in the context of 2D and 3D image reconstruction
using real images from the ImageNet database. We also apply the framework to
analyze a data set from retinal optical coherence tomography
Deep Learning in Cardiology
The medical field is creating large amount of data that physicians are unable
to decipher and use efficiently. Moreover, rule-based expert systems are
inefficient in solving complicated medical tasks or for creating insights using
big data. Deep learning has emerged as a more accurate and effective technology
in a wide range of medical problems such as diagnosis, prediction and
intervention. Deep learning is a representation learning method that consists
of layers that transform the data non-linearly, thus, revealing hierarchical
relationships and structures. In this review we survey deep learning
application papers that use structured data, signal and imaging modalities from
cardiology. We discuss the advantages and limitations of applying deep learning
in cardiology that also apply in medicine in general, while proposing certain
directions as the most viable for clinical use.Comment: 27 pages, 2 figures, 10 table
A fast patch-dictionary method for whole image recovery
Various algorithms have been proposed for dictionary learning. Among those
for image processing, many use image patches to form dictionaries. This paper
focuses on whole-image recovery from corrupted linear measurements. We address
the open issue of representing an image by overlapping patches: the overlapping
leads to an excessive number of dictionary coefficients to determine. With very
few exceptions, this issue has limited the applications of image-patch methods
to the local kind of tasks such as denoising, inpainting, cartoon-texture
decomposition, super-resolution, and image deblurring, for which one can
process a few patches at a time. Our focus is global imaging tasks such as
compressive sensing and medical image recovery, where the whole image is
encoded together, making it either impossible or very ineffective to update a
few patches at a time.
Our strategy is to divide the sparse recovery into multiple subproblems, each
of which handles a subset of non-overlapping patches, and then the results of
the subproblems are averaged to yield the final recovery. This simple strategy
is surprisingly effective in terms of both quality and speed. In addition, we
accelerate computation of the learned dictionary by applying a recent block
proximal-gradient method, which not only has a lower per-iteration complexity
but also takes fewer iterations to converge, compared to the current
state-of-the-art. We also establish that our algorithm globally converges to a
stationary point. Numerical results on synthetic data demonstrate that our
algorithm can recover a more faithful dictionary than two state-of-the-art
methods.
Combining our whole-image recovery and dictionary-learning methods, we
numerically simulate image inpainting, compressive sensing recovery, and
deblurring. Our recovery is more faithful than those of a total variation
method and a method based on overlapping patches
Recent Progress in Image Deblurring
This paper comprehensively reviews the recent development of image
deblurring, including non-blind/blind, spatially invariant/variant deblurring
techniques. Indeed, these techniques share the same objective of inferring a
latent sharp image from one or several corresponding blurry images, while the
blind deblurring techniques are also required to derive an accurate blur
kernel. Considering the critical role of image restoration in modern imaging
systems to provide high-quality images under complex environments such as
motion, undesirable lighting conditions, and imperfect system components, image
deblurring has attracted growing attention in recent years. From the viewpoint
of how to handle the ill-posedness which is a crucial issue in deblurring
tasks, existing methods can be grouped into five categories: Bayesian inference
framework, variational methods, sparse representation-based methods,
homography-based modeling, and region-based methods. In spite of achieving a
certain level of development, image deblurring, especially the blind case, is
limited in its success by complex application conditions which make the blur
kernel hard to obtain and be spatially variant. We provide a holistic
understanding and deep insight into image deblurring in this review. An
analysis of the empirical evidence for representative methods, practical
issues, as well as a discussion of promising future directions are also
presented.Comment: 53 pages, 17 figure
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