2,224 research outputs found
Sparse Signal Processing Concepts for Efficient 5G System Design
As it becomes increasingly apparent that 4G will not be able to meet the
emerging demands of future mobile communication systems, the question what
could make up a 5G system, what are the crucial challenges and what are the key
drivers is part of intensive, ongoing discussions. Partly due to the advent of
compressive sensing, methods that can optimally exploit sparsity in signals
have received tremendous attention in recent years. In this paper we will
describe a variety of scenarios in which signal sparsity arises naturally in 5G
wireless systems. Signal sparsity and the associated rich collection of tools
and algorithms will thus be a viable source for innovation in 5G wireless
system design. We will discribe applications of this sparse signal processing
paradigm in MIMO random access, cloud radio access networks, compressive
channel-source network coding, and embedded security. We will also emphasize
important open problem that may arise in 5G system design, for which sparsity
will potentially play a key role in their solution.Comment: 18 pages, 5 figures, accepted for publication in IEEE Acces
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Structured Sub-Nyquist Sampling with Applications in Compressive Toeplitz Covariance Estimation, Super-Resolution and Phase Retrieval
Sub-Nyquist sampling has received a huge amount of interest in the past decade. In classical compressed sensing theory, if the measurement procedure satisfies a particular condition known as Restricted Isometry Property (RIP), we can achieve stable recovery of signals of low-dimensional intrinsic structures with an order-wise optimal sample size. Such low-dimensional structures include sparse and low rank for both vector and matrix cases. The main drawback of conventional compressed sensing theory is that random measurements are required to ensure the RIP property. However, in many applications such as imaging and array signal processing, applying independent random measurements may not be practical as the systems are deterministic. Moreover, random measurements based compressed sensing always exploits convex programs for signal recovery even in the noiseless case, and solving those programs is computationally intensive if the ambient dimension is large, especially in the matrix case. The main contribution of this dissertation is that we propose a deterministic sub-Nyquist sampling framework for compressing the structured signal and come up with computationally efficient algorithms. Besides widely studied sparse and low-rank structures, we particularly focus on the cases that the signals of interest are stationary or the measurements are of Fourier type. The key difference between our work from classical compressed sensing theory is that we explicitly exploit the second-order statistics of the signals, and study the equivalent quadratic measurement model in the correlation domain. The essential observation made in this dissertation is that a difference/sum coarray structure will arise from the quadratic model if the measurements are of Fourier type. With these observations, we are able to achieve a better compression rate for covariance estimation, identify more sources in array signal processing or recover the signals of larger sparsity. In this dissertation, we will first study the problem of Toeplitz covariance estimation. In particular, we will show how to achieve an order-wise optimal compression rate using the idea of sparse arrays in both general and low-rank cases. Then, an analysis framework of super-resolution with positivity constraint is established. We will present fundamental robustness guarantees, efficient algorithms and applications in practices. Next, we will study the problem of phase-retrieval for which we successfully apply the sparse array ideas by fully exploiting the quadratic measurement model. We achieve near-optimal sample complexity for both sparse and general cases with practical Fourier measurements and provide efficient and deterministic recovery algorithms. In the end, we will further elaborate on the essential role of non-negative constraint in underdetermined inverse problems. In particular, we will analyze the nonlinear co-array interpolation problem and develop a universal upper bound of the interpolation error. Bilinear problem with non-negative constraint will be considered next and the exact characterization of the ambiguous solutions will be established for the first time in literature. At last, we will show how to apply the nested array idea to solve real problems such as Kriging. Using spatial correlation information, we are able to have a stable estimate of the field of interest with fewer sensors than classic methodologies. Extensive numerical experiments are implemented to demonstrate our theoretical claims
Incremental and Adaptive L1-Norm Principal Component Analysis: Novel Algorithms and Applications
L1-norm Principal-Component Analysis (L1-PCA) is known to attain remarkable resistance against faulty/corrupted points among the processed data. However, computing L1-PCA of “big data” with large number of measurements and/or dimensions may be computationally impractical. This work proposes new algorithmic solutions for incremental and adaptive L1-PCA. The first algorithm computes L1-PCA incrementally, processing one measurement at a time, with very low computational and memory requirements; thus, it is appropriate for big data and big streaming data applications. The second algorithm combines the merits of the first one with additional ability to track changes in the nominal signal subspace by revising the computed L1-PCA as new measurements arrive, demonstrating both robustness against outliers and adaptivity to signal-subspace changes. The proposed algorithms are evaluated in an array of experimental studies on subspace estimation, video surveillance (foreground/background separation), image conditioning, and direction-of-arrival (DoA) estimation
Side information in robust principal component analysis: algorithms and applications
Dimensionality reduction and noise removal are fundamental machine learning tasks that are vital to artificial intelligence applications. Principal component analysis has long been utilised in computer vision to achieve the above mentioned goals. Recently, it has been enhanced in terms of robustness to outliers in robust principal component analysis. Both convex and non-convex programs have been developed to solve this new formulation, some with exact convergence guarantees. Its effectiveness can be witnessed in image and video applications ranging from image denoising and alignment to background separation and face recognition. However, robust principal component analysis is by no means perfect. This dissertation identifies its limitations, explores various promising options for improvement and validates the proposed algorithms on both synthetic and real-world datasets.
Common algorithms approximate the NP-hard formulation of robust principal component analysis with convex envelopes. Though under certain assumptions exact recovery can be guaranteed, the relaxation margin is too big to be squandered. In this work, we propose to apply gradient descent on the Burer-Monteiro bilinear matrix factorisation to squeeze this margin given available subspaces. This non-convex approach improves upon conventional convex approaches both in terms of accuracy and speed. On the other hand, oftentimes there is accompanying side information when an observation is made. The ability to assimilate such auxiliary sources of data can ameliorate the recovery process. In this work, we investigate in-depth such possibilities for incorporating side information in restoring the true underlining low-rank component from gross sparse noise. Lastly, tensors, also known as multi-dimensional arrays, represent real-world data more naturally than matrices. It is thus advantageous to adapt robust principal component analysis to tensors. Since there is no exact equivalence between tensor rank and matrix rank, we employ the notions of Tucker rank and CP rank as our optimisation objectives. Overall, this dissertation carefully defines the problems when facing real-world computer vision challenges, extensively and impartially evaluates the state-of-the-art approaches, proposes novel solutions and provides sufficient validations on both simulated data and popular real-world datasets for various mainstream computer vision tasks.Open Acces
Topology optimization for inverse magnetostatics as sparse regression: application to electromagnetic coils for stellarators
Topology optimization, a technique to determine where material should be
placed within a predefined volume in order to minimize a physical objective, is
used across a wide range of scientific fields and applications. A general
application for topology optimization is inverse magnetostatics; a desired
magnetic field is prescribed, and a distribution of steady currents is computed
to produce that target field. In the present work, electromagnetic coils are
designed by magnetostatic topology optimization, using volume elements (voxels)
of electric current, constrained so the current is divergence-free. Compared to
standard electromagnet shape optimization, our method has the advantage that
the nonlinearity in the Biot-Savart law with respect to position is avoided,
enabling convex cost functions and a useful reformulation of topology
optimization as sparse regression. To demonstrate, we consider the application
of designing electromagnetic coils for a class of plasma experiments known as
stellarators. We produce topologically-exotic coils for several new stellarator
designs and show that these solutions can be interpolated into a filamentary
representation and then further optimized
Support matrix machine: A review
Support vector machine (SVM) is one of the most studied paradigms in the
realm of machine learning for classification and regression problems. It relies
on vectorized input data. However, a significant portion of the real-world data
exists in matrix format, which is given as input to SVM by reshaping the
matrices into vectors. The process of reshaping disrupts the spatial
correlations inherent in the matrix data. Also, converting matrices into
vectors results in input data with a high dimensionality, which introduces
significant computational complexity. To overcome these issues in classifying
matrix input data, support matrix machine (SMM) is proposed. It represents one
of the emerging methodologies tailored for handling matrix input data. The SMM
method preserves the structural information of the matrix data by using the
spectral elastic net property which is a combination of the nuclear norm and
Frobenius norm. This article provides the first in-depth analysis of the
development of the SMM model, which can be used as a thorough summary by both
novices and experts. We discuss numerous SMM variants, such as robust, sparse,
class imbalance, and multi-class classification models. We also analyze the
applications of the SMM model and conclude the article by outlining potential
future research avenues and possibilities that may motivate academics to
advance the SMM algorithm
Laterally constrained low-rank seismic data completion via cyclic-shear transform
A crucial step in seismic data processing consists in reconstructing the
wavefields at spatial locations where faulty or absent sources and/or receivers
result in missing data. Several developments in seismic acquisition and
interpolation strive to restore signals fragmented by sampling limitations;
still, seismic data frequently remain poorly sampled in the source, receiver,
or both coordinates. An intrinsic limitation of real-life dense acquisition
systems, which are often exceedingly expensive, is that they remain unable to
circumvent various physical and environmental obstacles, ultimately hindering a
proper recording scheme. In many situations, when the preferred reconstruction
method fails to render the actual continuous signals, subsequent imaging
studies are negatively affected by sampling artefacts. A recent alternative
builds on low-rank completion techniques to deliver superior restoration
results on seismic data, paving the way for data kernel compression that can
potentially unlock multiple modern processing methods so far prohibited in 3D
field scenarios. In this work, we propose a novel transform domain revealing
the low-rank character of seismic data that prevents the inherent matrix
enlargement introduced when the data are sorted in the midpoint-offset domain
and develop a robust extension of the current matrix completion framework to
account for lateral physical constraints that ensure a degree of proximity
similarity among neighbouring points. Our strategy successfully interpolates
missing sources and receivers simultaneously in synthetic and field data
Sparse Proteomics Analysis - A compressed sensing-based approach for feature selection and classification of high-dimensional proteomics mass spectrometry data
Background: High-throughput proteomics techniques, such as mass spectrometry
(MS)-based approaches, produce very high-dimensional data-sets. In a clinical
setting one is often interested in how mass spectra differ between patients of
different classes, for example spectra from healthy patients vs. spectra from
patients having a particular disease. Machine learning algorithms are needed to
(a) identify these discriminating features and (b) classify unknown spectra
based on this feature set. Since the acquired data is usually noisy, the
algorithms should be robust against noise and outliers, while the identified
feature set should be as small as possible.
Results: We present a new algorithm, Sparse Proteomics Analysis (SPA), based
on the theory of compressed sensing that allows us to identify a minimal
discriminating set of features from mass spectrometry data-sets. We show (1)
how our method performs on artificial and real-world data-sets, (2) that its
performance is competitive with standard (and widely used) algorithms for
analyzing proteomics data, and (3) that it is robust against random and
systematic noise. We further demonstrate the applicability of our algorithm to
two previously published clinical data-sets
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