134,796 research outputs found
MIMO decision feedback equalization from an Hâ perspective
We approach the multiple input multiple output (MIMO) decision feedback equalization (DFE) problem in digital communications from an Hâ estimation point of view. Using the standard (and simplifying) assumption that all previous decisions are correct, we obtain an explicit parameterization of all Hâ optimal DFEs. In particular, we show that, under the above assumption, minimum mean square error (MMSE) DFEs are Hâ optimal. The Hâ approach also suggests a method for dealing with errors in previous decisions
Projection-Based and Look Ahead Strategies for Atom Selection
In this paper, we improve iterative greedy search algorithms in which atoms
are selected serially over iterations, i.e., one-by-one over iterations. For
serial atom selection, we devise two new schemes to select an atom from a set
of potential atoms in each iteration. The two new schemes lead to two new
algorithms. For both the algorithms, in each iteration, the set of potential
atoms is found using a standard matched filter. In case of the first scheme, we
propose an orthogonal projection strategy that selects an atom from the set of
potential atoms. Then, for the second scheme, we propose a look ahead strategy
such that the selection of an atom in the current iteration has an effect on
the future iterations. The use of look ahead strategy requires a higher
computational resource. To achieve a trade-off between performance and
complexity, we use the two new schemes in cascade and develop a third new
algorithm. Through experimental evaluations, we compare the proposed algorithms
with existing greedy search and convex relaxation algorithms.Comment: sparsity, compressive sensing; IEEE Trans on Signal Processing 201
A cyclo-stationary complex multichannel wiener filter for the prediction of wind speed and direction
This paper develops a linear predictor for application to wind speed and direction forecasting in time and across different sites. The wind speed and direction are modelled via the magnitude and phase of a complex-valued time-series. A multichannel adaptive filter is set to predict this signal, based on its past values and the spatio-temporal correlation between wind signals measured at numerous geographical locations. The time-varying nature of the underlying system and the annual cycle of seasons motivates the development of a cyclo-stationary Wiener filter, which is tested on hourly mean wind speed and direction data from 13 weather stations across the UK, and shown to provide an improvement over both stationary Wiener filtering and a recent auto-regressive approach
Bayesian off-line detection of multiple change-points corrupted by multiplicative noise : application to SAR image edge detection
This paper addresses the problem of Bayesian off-line change-point detection in synthetic aperture radar images. The minimum mean square error and maximum a posteriori estimators of the changepoint positions are studied. Both estimators cannot be implemented because of optimization or integration problems. A practical implementation using Markov chain Monte Carlo methods is proposed. This implementation requires a priori knowledge of the so-called hyperparameters. A hyperparameter estimation procedure is proposed that alleviates the requirement of knowing the values of the hyperparameters. Simulation results on synthetic signals and synthetic aperture radar images are presented
Atomic norm denoising with applications to line spectral estimation
Motivated by recent work on atomic norms in inverse problems, we propose a
new approach to line spectral estimation that provides theoretical guarantees
for the mean-squared-error (MSE) performance in the presence of noise and
without knowledge of the model order. We propose an abstract theory of
denoising with atomic norms and specialize this theory to provide a convex
optimization problem for estimating the frequencies and phases of a mixture of
complex exponentials. We show that the associated convex optimization problem
can be solved in polynomial time via semidefinite programming (SDP). We also
show that the SDP can be approximated by an l1-regularized least-squares
problem that achieves nearly the same error rate as the SDP but can scale to
much larger problems. We compare both SDP and l1-based approaches with
classical line spectral analysis methods and demonstrate that the SDP
outperforms the l1 optimization which outperforms MUSIC, Cadzow's, and Matrix
Pencil approaches in terms of MSE over a wide range of signal-to-noise ratios.Comment: 27 pages, 10 figures. A preliminary version of this work appeared in
the Proceedings of the 49th Annual Allerton Conference in September 2011.
Numerous numerical experiments added to this version in accordance with
suggestions by anonymous reviewer
Non-convex Optimization for Machine Learning
A vast majority of machine learning algorithms train their models and perform
inference by solving optimization problems. In order to capture the learning
and prediction problems accurately, structural constraints such as sparsity or
low rank are frequently imposed or else the objective itself is designed to be
a non-convex function. This is especially true of algorithms that operate in
high-dimensional spaces or that train non-linear models such as tensor models
and deep networks.
The freedom to express the learning problem as a non-convex optimization
problem gives immense modeling power to the algorithm designer, but often such
problems are NP-hard to solve. A popular workaround to this has been to relax
non-convex problems to convex ones and use traditional methods to solve the
(convex) relaxed optimization problems. However this approach may be lossy and
nevertheless presents significant challenges for large scale optimization.
On the other hand, direct approaches to non-convex optimization have met with
resounding success in several domains and remain the methods of choice for the
practitioner, as they frequently outperform relaxation-based techniques -
popular heuristics include projected gradient descent and alternating
minimization. However, these are often poorly understood in terms of their
convergence and other properties.
This monograph presents a selection of recent advances that bridge a
long-standing gap in our understanding of these heuristics. The monograph will
lead the reader through several widely used non-convex optimization techniques,
as well as applications thereof. The goal of this monograph is to both,
introduce the rich literature in this area, as well as equip the reader with
the tools and techniques needed to analyze these simple procedures for
non-convex problems.Comment: The official publication is available from now publishers via
http://dx.doi.org/10.1561/220000005
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