11,134 research outputs found
Image reconstruction by domain transform manifold learning
Image reconstruction plays a critical role in the implementation of all
contemporary imaging modalities across the physical and life sciences including
optical, MRI, CT, PET, and radio astronomy. During an image acquisition, the
sensor encodes an intermediate representation of an object in the sensor
domain, which is subsequently reconstructed into an image by an inversion of
the encoding function. Image reconstruction is challenging because analytic
knowledge of the inverse transform may not exist a priori, especially in the
presence of sensor non-idealities and noise. Thus, the standard reconstruction
approach involves approximating the inverse function with multiple ad hoc
stages in a signal processing chain whose composition depends on the details of
each acquisition strategy, and often requires expert parameter tuning to
optimize reconstruction performance. We present here a unified framework for
image reconstruction, AUtomated TransfOrm by Manifold APproximation (AUTOMAP),
which recasts image reconstruction as a data-driven, supervised learning task
that allows a mapping between sensor and image domain to emerge from an
appropriate corpus of training data. We implement AUTOMAP with a deep neural
network and exhibit its flexibility in learning reconstruction transforms for a
variety of MRI acquisition strategies, using the same network architecture and
hyperparameters. We further demonstrate its efficiency in sparsely representing
transforms along low-dimensional manifolds, resulting in superior immunity to
noise and reconstruction artifacts compared with conventional handcrafted
reconstruction methods. In addition to improving the reconstruction performance
of existing acquisition methodologies, we anticipate accelerating the discovery
of new acquisition strategies across modalities as the burden of reconstruction
becomes lifted by AUTOMAP and learned-reconstruction approaches.Comment: 18 pages, 4 figure
Spatio-Temporal Deep Learning-Based Undersampling Artefact Reduction for 2D Radial Cine MRI with Limited Data
In this work we reduce undersampling artefacts in two-dimensional ()
golden-angle radial cine cardiac MRI by applying a modified version of the
U-net. We train the network on spatio-temporal slices which are previously
extracted from the image sequences. We compare our approach to two and a
Deep Learning-based post processing methods and to three iterative
reconstruction methods for dynamic cardiac MRI. Our method outperforms the
spatially trained U-net and the spatio-temporal U-net. Compared to the
spatio-temporal U-net, our method delivers comparable results, but with
shorter training times and less training data. Compared to the Compressed
Sensing-based methods -FOCUSS and a total variation regularised
reconstruction approach, our method improves image quality with respect to all
reported metrics. Further, it achieves competitive results when compared to an
iterative reconstruction method based on adaptive regularization with
Dictionary Learning and total variation, while only requiring a small fraction
of the computational time. A persistent homology analysis demonstrates that the
data manifold of the spatio-temporal domain has a lower complexity than the
spatial domain and therefore, the learning of a projection-like mapping is
facilitated. Even when trained on only one single subject without
data-augmentation, our approach yields results which are similar to the ones
obtained on a large training dataset. This makes the method particularly
suitable for training a network on limited training data. Finally, in contrast
to the spatial U-net, our proposed method is shown to be naturally robust
with respect to image rotation in image space and almost achieves
rotation-equivariance where neither data-augmentation nor a particular network
design are required.Comment: To be published in IEEE Transactions on Medical Imagin
Sequential Principal Curves Analysis
This work includes all the technical details of the Sequential Principal
Curves Analysis (SPCA) in a single document. SPCA is an unsupervised nonlinear
and invertible feature extraction technique. The identified curvilinear
features can be interpreted as a set of nonlinear sensors: the response of each
sensor is the projection onto the corresponding feature. Moreover, it can be
easily tuned for different optimization criteria; e.g. infomax, error
minimization, decorrelation; by choosing the right way to measure distances
along each curvilinear feature. Even though proposed in [Laparra et al. Neural
Comp. 12] and shown to work in multiple modalities in [Laparra and Malo
Frontiers Hum. Neuro. 15], the SPCA framework has its original roots in the
nonlinear ICA algorithm in [Malo and Gutierrez Network 06]. Later on, the SPCA
philosophy for nonlinear generalization of PCA originated substantially faster
alternatives at the cost of introducing different constraints in the model.
Namely, the Principal Polynomial Analysis (PPA) [Laparra et al. IJNS 14], and
the Dimensionality Reduction via Regression (DRR) [Laparra et al. IEEE TGRS
15]. This report illustrates the reasons why we developed such family and is
the appropriate technical companion for the missing details in [Laparra et al.,
NeCo 12, Laparra and Malo, Front.Hum.Neuro. 15]. See also the data, code and
examples in the dedicated sites http://isp.uv.es/spca.html and
http://isp.uv.es/after effects.htmlComment: 17 pages, 14 figs., 72 ref
Bi-Linear Modeling of Data Manifolds for Dynamic-MRI Recovery
This paper puts forth a novel bi-linear modeling framework for data recovery
via manifold-learning and sparse-approximation arguments and considers its
application to dynamic magnetic-resonance imaging (dMRI). Each temporal-domain
MR image is viewed as a point that lies onto or close to a smooth manifold, and
landmark points are identified to describe the point cloud concisely. To
facilitate computations, a dimensionality reduction module generates
low-dimensional/compressed renditions of the landmark points. Recovery of the
high-fidelity MRI data is realized by solving a non-convex minimization task
for the linear decompression operator and those affine combinations of landmark
points which locally approximate the latent manifold geometry. An algorithm
with guaranteed convergence to stationary solutions of the non-convex
minimization task is also provided. The aforementioned framework exploits the
underlying spatio-temporal patterns and geometry of the acquired data without
any prior training on external data or information. Extensive numerical results
on simulated as well as real cardiac-cine and perfusion MRI data illustrate
noteworthy improvements of the advocated machine-learning framework over
state-of-the-art reconstruction techniques
Principal Polynomial Analysis
This paper presents a new framework for manifold learning based on a sequence
of principal polynomials that capture the possibly nonlinear nature of the
data. The proposed Principal Polynomial Analysis (PPA) generalizes PCA by
modeling the directions of maximal variance by means of curves, instead of
straight lines. Contrarily to previous approaches, PPA reduces to performing
simple univariate regressions, which makes it computationally feasible and
robust. Moreover, PPA shows a number of interesting analytical properties.
First, PPA is a volume-preserving map, which in turn guarantees the existence
of the inverse. Second, such an inverse can be obtained in closed form.
Invertibility is an important advantage over other learning methods, because it
permits to understand the identified features in the input domain where the
data has physical meaning. Moreover, it allows to evaluate the performance of
dimensionality reduction in sensible (input-domain) units. Volume preservation
also allows an easy computation of information theoretic quantities, such as
the reduction in multi-information after the transform. Third, the analytical
nature of PPA leads to a clear geometrical interpretation of the manifold: it
allows the computation of Frenet-Serret frames (local features) and of
generalized curvatures at any point of the space. And fourth, the analytical
Jacobian allows the computation of the metric induced by the data, thus
generalizing the Mahalanobis distance. These properties are demonstrated
theoretically and illustrated experimentally. The performance of PPA is
evaluated in dimensionality and redundancy reduction, in both synthetic and
real datasets from the UCI repository
Sampling in the Analysis Transform Domain
Many signal and image processing applications have benefited remarkably from
the fact that the underlying signals reside in a low dimensional subspace. One
of the main models for such a low dimensionality is the sparsity one. Within
this framework there are two main options for the sparse modeling: the
synthesis and the analysis ones, where the first is considered the standard
paradigm for which much more research has been dedicated. In it the signals are
assumed to have a sparse representation under a given dictionary. On the other
hand, in the analysis approach the sparsity is measured in the coefficients of
the signal after applying a certain transformation, the analysis dictionary, on
it. Though several algorithms with some theory have been developed for this
framework, they are outnumbered by the ones proposed for the synthesis
methodology.
Given that the analysis dictionary is either a frame or the two dimensional
finite difference operator, we propose a new sampling scheme for signals from
the analysis model that allows to recover them from their samples using any
existing algorithm from the synthesis model. The advantage of this new sampling
strategy is that it makes the existing synthesis methods with their theory also
available for signals from the analysis framework.Comment: 13 Pages, 2 figure
Dimensionality Reduction via Regression in Hyperspectral Imagery
This paper introduces a new unsupervised method for dimensionality reduction
via regression (DRR). The algorithm belongs to the family of invertible
transforms that generalize Principal Component Analysis (PCA) by using
curvilinear instead of linear features. DRR identifies the nonlinear features
through multivariate regression to ensure the reduction in redundancy between
he PCA coefficients, the reduction of the variance of the scores, and the
reduction in the reconstruction error. More importantly, unlike other nonlinear
dimensionality reduction methods, the invertibility, volume-preservation, and
straightforward out-of-sample extension, makes DRR interpretable and easy to
apply. The properties of DRR enable learning a more broader class of data
manifolds than the recently proposed Non-linear Principal Components Analysis
(NLPCA) and Principal Polynomial Analysis (PPA). We illustrate the performance
of the representation in reducing the dimensionality of remote sensing data. In
particular, we tackle two common problems: processing very high dimensional
spectral information such as in hyperspectral image sounding data, and dealing
with spatial-spectral image patches of multispectral images. Both settings pose
collinearity and ill-determination problems. Evaluation of the expressive power
of the features is assessed in terms of truncation error, estimating
atmospheric variables, and surface land cover classification error. Results
show that DRR outperforms linear PCA and recently proposed invertible
extensions based on neural networks (NLPCA) and univariate regressions (PPA).Comment: 12 pages, 6 figures, 62 reference
Low dose CT reconstruction assisted by an image manifold prior
X-ray Computed Tomography (CT) is an important tool in medical imaging to
obtain a direct visualization of patient anatomy. However, the x-ray radiation
exposure leads to the concern of lifetime cancer risk. Low-dose CT scan can
reduce the radiation exposure to patient while the image quality is usually
degraded due to the appearance of noise and artifacts. Numerous studies have
been conducted to regularize CT image for better image quality. Yet, exploring
the underlying manifold where real CT images residing on is still an open
problem. In this paper, we propose a fully data-driven manifold learning
approach by incorporating the emerging deep-learning technology. An
encoder-decoder convolutional neural network has been established to map a CT
image to the inherent low-dimensional manifold, as well as to restore the CT
image from its corresponding manifold representation. A novel reconstruction
algorithm assisted by the leant manifold prior has been developed to achieve
high quality low-dose CT reconstruction. In order to demonstrate the
effectiveness of the proposed framework, network training, testing, and
comprehensive simulation study have been performed using patient abdomen CT
images. The trained encoder-decoder CNN is capable of restoring high-quality CT
images with average error of ~20 HU. Furthermore, the proposed manifold prior
assisted reconstruction scheme achieves high-quality low-dose CT
reconstruction, with average reconstruction error of < 30 HU, more than five
times and two times lower than that of filtered back projection method and
total-variation based iterative reconstruction method, respectively
A Tale of Two Bases: Local-Nonlocal Regularization on Image Patches with Convolution Framelets
We propose an image representation scheme combining the local and nonlocal
characterization of patches in an image. Our representation scheme can be shown
to be equivalent to a tight frame constructed from convolving local bases (e.g.
wavelet frames, discrete cosine transforms, etc.) with nonlocal bases (e.g.
spectral basis induced by nonlinear dimension reduction on patches), and we
call the resulting frame elements {\it convolution framelets}. Insight gained
from analyzing the proposed representation leads to a novel interpretation of a
recent high-performance patch-based image inpainting algorithm using Point
Integral Method (PIM) and Low Dimension Manifold Model (LDMM) [Osher, Shi and
Zhu, 2016]. In particular, we show that LDMM is a weighted
-regularization on the coefficients obtained by decomposing images into
linear combinations of convolution framelets; based on this understanding, we
extend the original LDMM to a reweighted version that yields further improved
inpainting results. In addition, we establish the energy concentration property
of convolution framelet coefficients for the setting where the local basis is
constructed from a given nonlocal basis via a linear reconstruction framework;
a generalization of this framework to unions of local embeddings can provide a
natural setting for interpreting BM3D, one of the state-of-the-art image
denoising algorithms
Video Compressive Sensing for Dynamic MRI
We present a video compressive sensing framework, termed kt-CSLDS, to
accelerate the image acquisition process of dynamic magnetic resonance imaging
(MRI). We are inspired by a state-of-the-art model for video compressive
sensing that utilizes a linear dynamical system (LDS) to model the motion
manifold. Given compressive measurements, the state sequence of an LDS can be
first estimated using system identification techniques. We then reconstruct the
observation matrix using a joint structured sparsity assumption. In particular,
we minimize an objective function with a mixture of wavelet sparsity and joint
sparsity within the observation matrix. We derive an efficient convex
optimization algorithm through alternating direction method of multipliers
(ADMM), and provide a theoretical guarantee for global convergence. We
demonstrate the performance of our approach for video compressive sensing, in
terms of reconstruction accuracy. We also investigate the impact of various
sampling strategies. We apply this framework to accelerate the acquisition
process of dynamic MRI and show it achieves the best reconstruction accuracy
with the least computational time compared with existing algorithms in the
literature.Comment: 30 pages, 9 figure
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