186 research outputs found
Capacity Bounds for Communication Systems with Quantization and Spectral Constraints
Low-resolution digital-to-analog and analog-to-digital converters (DACs and
ADCs) have attracted considerable attention in efforts to reduce power
consumption in millimeter wave (mmWave) and massive MIMO systems. This paper
presents an information-theoretic analysis with capacity bounds for classes of
linear transceivers with quantization. The transmitter modulates symbols via a
unitary transform followed by a DAC and the receiver employs an ADC followed by
the inverse unitary transform. If the unitary transform is set to an FFT
matrix, the model naturally captures filtering and spectral constraints which
are essential to model in any practical transceiver. In particular, this model
allows studying the impact of quantization on out-of-band emission constraints.
In the limit of a large random unitary transform, it is shown that the effect
of quantization can be precisely described via an additive Gaussian noise
model. This model in turn leads to simple and intuitive expressions for the
power spectrum of the transmitted signal and a lower bound to the capacity with
quantization. Comparison with non-quantized capacity and a capacity upper bound
that does not make linearity assumptions suggests that while low resolution
quantization has minimal impact on the achievable rate at typical parameters in
5G systems today, satisfying out-of-band emissions are potentially much more of
a challenge.Comment: Appears in the Proceedings of IEEE International Symposium on
Information Theory (ISIT) 202
The Mutual Information in Random Linear Estimation Beyond i.i.d. Matrices
There has been definite progress recently in proving the variational
single-letter formula given by the heuristic replica method for various
estimation problems. In particular, the replica formula for the mutual
information in the case of noisy linear estimation with random i.i.d. matrices,
a problem with applications ranging from compressed sensing to statistics, has
been proven rigorously. In this contribution we go beyond the restrictive
i.i.d. matrix assumption and discuss the formula proposed by Takeda, Uda,
Kabashima and later by Tulino, Verdu, Caire and Shamai who used the replica
method. Using the recently introduced adaptive interpolation method and random
matrix theory, we prove this formula for a relevant large sub-class of
rotationally invariant matrices.Comment: Presented at the 2018 IEEE International Symposium on Information
Theory (ISIT
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
Convergence of Smoothed Empirical Measures with Applications to Entropy Estimation
This paper studies convergence of empirical measures smoothed by a Gaussian
kernel. Specifically, consider approximating , for
, by
, where is the empirical measure,
under different statistical distances. The convergence is examined in terms of
the Wasserstein distance, total variation (TV), Kullback-Leibler (KL)
divergence, and -divergence. We show that the approximation error under
the TV distance and 1-Wasserstein distance () converges at rate
in remarkable contrast to a typical
rate for unsmoothed (and ). For the
KL divergence, squared 2-Wasserstein distance (), and
-divergence, the convergence rate is , but only if
achieves finite input-output mutual information across the additive
white Gaussian noise channel. If the latter condition is not met, the rate
changes to for the KL divergence and , while
the -divergence becomes infinite - a curious dichotomy. As a main
application we consider estimating the differential entropy
in the high-dimensional regime. The distribution
is unknown but i.i.d samples from it are available. We first show that
any good estimator of must have sample complexity
that is exponential in . Using the empirical approximation results we then
show that the absolute-error risk of the plug-in estimator converges at the
parametric rate , thus establishing the minimax
rate-optimality of the plug-in. Numerical results that demonstrate a
significant empirical superiority of the plug-in approach to general-purpose
differential entropy estimators are provided.Comment: arXiv admin note: substantial text overlap with arXiv:1810.1158
Subspace Structure Regularized Nonnegative Matrix Factorization for Hyperspectral Unmixing
Hyperspectral unmixing is a crucial task for hyperspectral images (HSI) processing, which estimates the proportions of constituent materials of a mixed pixel. Usually, the mixed pixels can be approximated using a linear mixing model. Since each material only occurs in a few pixels in real HSI, sparse nonnegative matrix factorization (NMF) and its extensions are widely used as solutions. Some recent works assume that materials are distributed in certain structures, which can be added as constraints to sparse NMF model. However, they only consider the spatial distribution within a local neighborhood and define the distribution structure manually, while ignoring the real distribution of materials that is diverse in different images. In this paper, we propose a new unmixing method that learns a subspace structure from the original image and incorporate it into the sparse NMF framework to promote unmixing performance. Based on the self-representation property of data points lying in the same subspace, the learned subspace structure can indicate the global similar graph of pixels that represents the real distribution of materials. Then the similar graph is used as a robust global spatial prior which is expected to be maintained in the decomposed abundance matrix. The experiments conducted on both simulated and real-world HSI datasets demonstrate the superior performance of our proposed method
Deep learning-based music source separation
Diese Dissertation befasst sich mit dem Problem der Trennung von Musikquellen durch den Einsatz von deep learning Methoden. Die auf deep learning basierende Trennung von Musikquellen wird unter drei Gesichtspunkten untersucht. Diese Perspektiven sind: die Signalverarbeitung, die neuronale Architektur und die Signaldarstellung. Aus der ersten Perspektive, soll verstanden werden, welche deep learning Modelle, die auf DNNs basieren, für die Aufgabe der Musikquellentrennung lernen, und ob es einen analogen Signalverarbeitungsoperator gibt, der die Funktionalität dieser Modelle charakterisiert. Zu diesem Zweck wird ein neuartiger Algorithmus vorgestellt. Der Algorithmus wird als NCA bezeichnet und destilliert ein optimiertes Trennungsmodell, das aus nicht-linearen Operatoren besteht, in einen einzigen linearen Operator, der leicht zu interpretieren ist. Aus der zweiten Perspektive, soll eine neuronale Netzarchitektur vorgeschlagen werden, die das zuvor erwähnte Konzept der Filterberechnung und -optimierung beinhaltet. Zu diesem Zweck wird die als Masker and Denoiser (MaD) bezeichnete neuronale Netzarchitektur vorgestellt. Die vorgeschlagene Architektur realisiert die Filteroperation unter Verwendung skip-filtering connections Verbindungen. Zusätzlich werden einige Inferenzstrategien und Optimierungsziele vorgeschlagen und diskutiert. Die Leistungsfähigkeit von MaD bei der Musikquellentrennung wird durch eine Reihe von Experimenten bewertet, die sowohl objektive als auch subjektive Bewertungsverfahren umfassen. Abschließend, der Schwerpunkt der dritten Perspektive liegt auf dem Einsatz von DNNs zum Erlernen von solchen Signaldarstellungen, für die Trennung von Musikquellen hilfreich sind. Zu diesem Zweck wird eine neue Methode vorgeschlagen. Die vorgeschlagene Methode verwendet ein neuartiges Umparametrisierungsschema und eine Kombination von Optimierungszielen. Die Umparametrisierung basiert sich auf sinusförmigen Funktionen, die interpretierbare DNN-Darstellungen fördern. Der durchgeführten Experimente deuten an, dass die vorgeschlagene Methode beim Erlernen interpretierbarer Darstellungen effizient eingesetzt werden kann, wobei der Filterprozess noch auf separate Musikquellen angewendet werden kann. Die Ergebnisse der durchgeführten Experimente deuten an, dass die vorgeschlagene Methode beim Erlernen interpretierbarer Darstellungen effizient eingesetzt werden kann, wobei der Filterprozess noch auf separate Musikquellen angewendet werden kann. Darüber hinaus der Einsatz von optimal transport (OT) Entfernungen als Optimierungsziele sind für die Berechnung additiver und klar strukturierter Signaldarstellungen.This thesis addresses the problem of music source separation using deep learning methods. The deep learning-based separation of music sources is examined from three angles. These angles are: the signal processing, the neural architecture, and the signal representation. From the first angle, it is aimed to understand what deep learning models, using deep neural networks (DNNs), learn for the task of music source separation, and if there is an analogous signal processing operator that characterizes the functionality of these models. To do so, a novel algorithm is presented. The algorithm, referred to as the neural couplings algorithm (NCA), distills an optimized separation model consisting of non-linear operators into a single linear operator that is easy to interpret. Using the NCA, it is shown that DNNs learn data-driven filters for singing voice separation, that can be assessed using signal processing. Moreover, by enabling DNNs to learn how to predict filters for source separation, DNNs capture the structure of the target source and learn robust filters. From the second angle, it is aimed to propose a neural network architecture that incorporates the aforementioned concept of filter prediction and optimization. For this purpose, the neural network architecture referred to as the Masker-and-Denoiser (MaD) is presented. The proposed architecture realizes the filtering operation using skip-filtering connections. Additionally, a few inference strategies and optimization objectives are proposed and discussed. The performance of MaD in music source separation is assessed by conducting a series of experiments that include both objective and subjective evaluation processes. Experimental results suggest that the MaD architecture, with some of the studied strategies, is applicable to realistic music recordings, and the MaD architecture has been considered one of the state-of-the-art approaches in the Signal Separation and Evaluation Campaign (SiSEC) 2018. Finally, the focus of the third angle is to employ DNNs for learning signal representations that are helpful for separating music sources. To that end, a new method is proposed using a novel re-parameterization scheme and a combination of optimization objectives. The re-parameterization is based on sinusoidal functions that promote interpretable DNN representations. Results from the conducted experimental procedure suggest that the proposed method can be efficiently employed in learning interpretable representations, where the filtering process can still be applied to separate music sources. Furthermore, the usage of optimal transport (OT) distances as optimization objectives is useful for computing additive and distinctly structured signal representations for various types of music sources
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