308 research outputs found
Dependent Nonparametric Bayesian Group Dictionary Learning for online reconstruction of Dynamic MR images
In this paper, we introduce a dictionary learning based approach applied to
the problem of real-time reconstruction of MR image sequences that are highly
undersampled in k-space. Unlike traditional dictionary learning, our method
integrates both global and patch-wise (local) sparsity information and
incorporates some priori information into the reconstruction process. Moreover,
we use a Dependent Hierarchical Beta-process as the prior for the group-based
dictionary learning, which adaptively infers the dictionary size and the
sparsity of each patch; and also ensures that similar patches are manifested in
terms of similar dictionary atoms. An efficient numerical algorithm based on
the alternating direction method of multipliers (ADMM) is also presented.
Through extensive experimental results we show that our proposed method
achieves superior reconstruction quality, compared to the other state-of-the-
art DL-based methods
A Hierarchical Bayesian Model for Frame Representation
In many signal processing problems, it may be fruitful to represent the
signal under study in a frame. If a probabilistic approach is adopted, it
becomes then necessary to estimate the hyper-parameters characterizing the
probability distribution of the frame coefficients. This problem is difficult
since in general the frame synthesis operator is not bijective. Consequently,
the frame coefficients are not directly observable. This paper introduces a
hierarchical Bayesian model for frame representation. The posterior
distribution of the frame coefficients and model hyper-parameters is derived.
Hybrid Markov Chain Monte Carlo algorithms are subsequently proposed to sample
from this posterior distribution. The generated samples are then exploited to
estimate the hyper-parameters and the frame coefficients of the target signal.
Validation experiments show that the proposed algorithms provide an accurate
estimation of the frame coefficients and hyper-parameters. Application to
practical problems of image denoising show the impact of the resulting Bayesian
estimation on the recovered signal quality
Communications-Inspired Projection Design with Application to Compressive Sensing
We consider the recovery of an underlying signal x \in C^m based on
projection measurements of the form y=Mx+w, where y \in C^l and w is
measurement noise; we are interested in the case l < m. It is assumed that the
signal model p(x) is known, and w CN(w;0,S_w), for known S_W. The objective is
to design a projection matrix M \in C^(l x m) to maximize key
information-theoretic quantities with operational significance, including the
mutual information between the signal and the projections I(x;y) or the Renyi
entropy of the projections h_a(y) (Shannon entropy is a special case). By
capitalizing on explicit characterizations of the gradients of the information
measures with respect to the projections matrix, where we also partially extend
the well-known results of Palomar and Verdu from the mutual information to the
Renyi entropy domain, we unveil the key operations carried out by the optimal
projections designs: mode exposure and mode alignment. Experiments are
considered for the case of compressive sensing (CS) applied to imagery. In this
context, we provide a demonstration of the performance improvement possible
through the application of the novel projection designs in relation to
conventional ones, as well as justification for a fast online projections
design method with which state-of-the-art adaptive CS signal recovery is
achieved.Comment: 25 pages, 7 figures, parts of material published in IEEE ICASSP 2012,
submitted to SIIM
Adaptive Sampling with Mobile Sensor Networks
Mobile sensor networks have unique advantages compared with wireless sensor networks. The mobility enables mobile sensors to flexibly reconfigure themselves to meet sensing requirements. In this dissertation, an adaptive sampling method for mobile sensor networks is presented. Based on the consideration of sensing resource constraints, computing abilities, and onboard energy limitations, the adaptive sampling method follows a down sampling scheme, which could reduce the total number of measurements, and lower sampling cost. Compressive sensing is a recently developed down sampling method, using a small number of randomly distributed measurements for signal reconstruction. However, original signals cannot be reconstructed using condensed measurements, as addressed by Shannon Sampling Theory. Measurements have to be processed under a sparse domain, and convex optimization methods should be applied to reconstruct original signals. Restricted isometry property would guarantee signals can be recovered with little information loss. While compressive sensing could effectively lower sampling cost, signal reconstruction is still a great research challenge. Compressive sensing always collects random measurements, whose information amount cannot be determined in prior. If each measurement is optimized as the most informative measurement, the reconstruction performance can perform much better.
Based on the above consideration, this dissertation is focusing on an adaptive sampling approach, which could find the most informative measurements in unknown environments and reconstruct original signals. With mobile sensors, measurements are collect sequentially, giving the chance to uniquely optimize each of them. When mobile sensors are about to collect a new measurement from the surrounding environments, existing information is shared among networked sensors so that each sensor would have a global view of the entire environment. Shared information is analyzed under Haar Wavelet domain, under which most nature signals appear sparse, to infer a model of the environments. The most informative measurements can be determined by optimizing model parameters. As a result, all the measurements collected by the mobile sensor network are the most informative measurements given existing information, and a perfect reconstruction would be expected.
To present the adaptive sampling method, a series of research issues will be addressed, including measurement evaluation and collection, mobile network establishment, data fusion, sensor motion, signal reconstruction, etc. Two dimensional scalar field will be reconstructed using the method proposed. Both single mobile sensors and mobile sensor networks will be deployed in the environment, and reconstruction performance of both will be compared.In addition, a particular mobile sensor, a quadrotor UAV is developed, so that the adaptive sampling method can be used in three dimensional scenarios
Robust and Efficient Inference of Scene and Object Motion in Multi-Camera Systems
Multi-camera systems have the ability to overcome some of the fundamental limitations of single camera based systems. Having multiple view points of a scene goes a long way in limiting the influence of field of view, occlusion, blur and poor resolution of an individual camera. This dissertation addresses robust and efficient inference of object motion and scene in multi-camera and multi-sensor systems.
The first part of the dissertation discusses the role of constraints introduced by projective imaging towards robust inference of multi-camera/sensor based object motion. We discuss the role of the homography and epipolar constraints for fusing object motion perceived by individual cameras. For planar scenes, the homography constraints provide a natural mechanism for data association. For scenes that are not planar, the epipolar constraint provides a weaker multi-view relationship. We use the epipolar constraint for tracking in multi-camera and multi-sensor networks. In particular, we show that the epipolar constraint reduces the dimensionality of the state space of the
problem by introducing a ``shared'' state space for the joint tracking problem. This allows for robust tracking even when one of the sensors fail due to poor SNR or occlusion.
The second part of the dissertation deals with challenges in the computational aspects of tracking algorithms that are common to such systems. Much of the inference in the multi-camera and multi-sensor networks deal with complex non-linear models corrupted with non-Gaussian noise. Particle filters provide approximate Bayesian inference in such settings. We analyze the computational drawbacks of traditional particle filtering algorithms, and present a method for implementing the particle filter using the Independent Metropolis Hastings sampler, that is highly amenable to pipelined implementations and parallelization. We analyze the implementations of the proposed algorithm, and in particular concentrate on implementations that have
minimum processing times.
The last part of the dissertation deals with the efficient sensing paradigm of compressing sensing (CS) applied to signals in imaging, such as natural images and reflectance fields. We propose a hybrid signal model on the assumption that most real-world signals exhibit subspace compressibility as well as sparse representations. We show that several real-world visual signals such as images, reflectance fields, videos etc., are better approximated by this hybrid of two models. We derive optimal hybrid linear projections of the signal and show that theoretical guarantees and algorithms designed for CS can be easily extended to hybrid subspace-compressive sensing. Such methods reduce the
amount of information sensed by a camera, and help in reducing the so called data deluge problem in large multi-camera systems
Hyperspectral Unmixing Overview: Geometrical, Statistical, and Sparse Regression-Based Approaches
Imaging spectrometers measure electromagnetic energy scattered in their
instantaneous field view in hundreds or thousands of spectral channels with
higher spectral resolution than multispectral cameras. Imaging spectrometers
are therefore often referred to as hyperspectral cameras (HSCs). Higher
spectral resolution enables material identification via spectroscopic analysis,
which facilitates countless applications that require identifying materials in
scenarios unsuitable for classical spectroscopic analysis. Due to low spatial
resolution of HSCs, microscopic material mixing, and multiple scattering,
spectra measured by HSCs are mixtures of spectra of materials in a scene. Thus,
accurate estimation requires unmixing. Pixels are assumed to be mixtures of a
few materials, called endmembers. Unmixing involves estimating all or some of:
the number of endmembers, their spectral signatures, and their abundances at
each pixel. Unmixing is a challenging, ill-posed inverse problem because of
model inaccuracies, observation noise, environmental conditions, endmember
variability, and data set size. Researchers have devised and investigated many
models searching for robust, stable, tractable, and accurate unmixing
algorithms. This paper presents an overview of unmixing methods from the time
of Keshava and Mustard's unmixing tutorial [1] to the present. Mixing models
are first discussed. Signal-subspace, geometrical, statistical, sparsity-based,
and spatial-contextual unmixing algorithms are described. Mathematical problems
and potential solutions are described. Algorithm characteristics are
illustrated experimentally.Comment: This work has been accepted for publication in IEEE Journal of
Selected Topics in Applied Earth Observations and Remote Sensin
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