arXiv research

This paper reconstructs complex graph signals using kernel methods on manifolds.

Paper introduces signal processing on cell complexes.

There are three equivalent ways of representing two jointly observed real-valued signals: as a bivariate vector signal, as a single complex-valued signal, or as two analytic signals known as the rotary components. Each representation has unique advantages depending on the system of interest and the application goals. I…

Tutorials on signal processing on higher-order networks like simplicial complexes and hypergraphs.

Proposes a probabilistic framework for stationary topological signals on simplicial complexes.

We study the problem of corrupted sensing, a generalization of compressed sensing in which one aims to recover a signal from a collection of corrupted or unreliable measurements. While an arbitrary signal cannot be recovered in the face of arbitrary corruption, tractable recovery is possible when both signal and corrup…

Optimal trend-following strategy uses simple EMA, avoiding complex cherry-picked signals.

The construction of synthetic complex-valued signals from real-valued observations is an important step in many time series analysis techniques. The most widely used approach is based on the Hilbert transform, which maps the real-valued signal into its quadrature component. In this paper, we define a probabilistic gene…

PolarBM models complex-valued audio signals in polar coordinates, improving over conventional methods.

Deep neural networks help recover two signals from noisy mixtures.

Hadamard Wirtinger Flow recovers sparse signals from fewer measurements.

This work optimizes signal estimation for sparse MRA with collision-free signals.

The relation between performance and stress is described by the Yerkes-Dodson Law but varies significantly between individuals. This paper describes a method for determining the individual optimal performance as a function of physiological signals. The method is based on attention and reasoning tests of increasing comp…

Proposes a new complex Gaussian distribution for better modeling of complex-valued signals.

This paper tackles non-convex phase retrieval with structured assumptions.

Novel algorithm learns sparse signal representations over topological spaces.

The problem of estimating the number of sources and their angles of arrival from a single antenna array observation has been an active area of research in the signal processing community for the last few decades. When the number of sources is large, the maximum likelihood estimator is intractable due to its very high c…

Complex-valued signals are used in the modeling of many systems in engineering and science, hence being of fundamental interest. Often, random complex-valued signals are considered to be proper. A proper complex random variable or process is uncorrelated with its complex conjugate. This assumption is a good model of th…

Detect anomalies in complex networks using topological subspace detectors.

Improved model for non-smooth signals with complex spectra.

We consider the problem of signal recovery on graphs as graphs model data with complex structure as signals on a graph. Graph signal recovery implies recovery of one or multiple smooth graph signals from noisy, corrupted, or incomplete measurements. We propose a graph signal model and formulate signal recovery as a cor…

We consider the problem of recovering a signal $\mathbf{x}^* \in \mathbf{R}^n$, from magnitude-only measurements $y_i = |\left\langle\mathbf{a}_i,\mathbf{x}^*\right\rangle|$ for $i=[m]$. Also called the phase retrieval, this is a fundamental challenge in bio-,astronomical imaging and speech processing. The problem abov…

A new neural network captures and explains trajectory patterns.

We propose a novel adaptive kernel based regression method for complex-valued signals: the generalized complex-valued kernel least-mean-square (gCKLMS). We borrow from the new results on widely linear reproducing kernel Hilbert space (WL-RKHS) for nonlinear regression and complex-valued signals, recently proposed by th…

This paper explores robust recovery of a superposition of $R$ distinct complex exponential functions from a few random Gaussian projections. We assume that the signal of interest is of $2N-1$ dimensional and $R<<2N-1$. This framework covers a large class of signals arising from real applications in biology, automation,…

While deep learning has received a surge of interest in a variety of fields in recent years, major deep learning models barely use complex numbers. However, speech, signal and audio data are naturally complex-valued after Fourier Transform, and studies have shown a potentially richer representation of complex nets. In …

New algorithm for decomposing multidimensional, non-stationary signals.

Neural process model improves real-time condition monitoring signal prediction.

Graph signal processing improves machine learning for network data.

Method recovers complex-valued signals from speckle-noised measurements.

Survey of complex-valued neural networks for improved performance.

This research improves asset life prediction by integrating deep learning with mixture distributions.

We present reconstruction algorithms for smooth signals with block sparsity from their compressed measurements. We tackle the issue of varying group size via group-sparse least absolute shrinkage selection operator (LASSO) as well as via latent group LASSO regularizations. We achieve smoothness in the signal via fusion…

In this paper, we develop a new framework for sensing and recovering structured signals. In contrast to compressive sensing (CS) systems that employ linear measurements, sparse representations, and computationally complex convex/greedy algorithms, we introduce a deep learning framework that supports both linear and mil…

Goal: This paper deals with the problems that some EEG signals have no good sparse representation and single channel processing is not computationally efficient in compressed sensing of multi-channel EEG signals. Methods: An optimization model with L0 norm and Schatten-0 norm is proposed to enforce cosparsity and low r…

We present a novel blind source separation (BSS) method, called information geometric blind source separation (IGBSS). Our formulation is based on the log-linear model equipped with a hierarchically structured sample space, which has theoretical guarantees to uniquely recover a set of source signals by minimizing the K…

Non-linear image reconstruction and signal analysis deal with complex inverse problems. To tackle such problems in a systematic way, I present information field theory (IFT) as a means of Bayesian, data based inference on spatially distributed signal fields. IFT is a statistical field theory, which permits the construc…

New method uses image registration to recover complex signals from amplitude data.

Nonnegative matrix factorization (NMF) is now a common tool for audio source separation. When learning NMF on large audio databases, one major drawback is that the complexity in time is O(FKN) when updating the dictionary (where (F;N) is the dimension of the input power spectrograms, and K the number of basis spectra),…

New AMP algorithms for rotationally invariant models with reduced complexity.

This work extends alpha-beta divergences to complex data and finds closed-form solutions.

Phase Modulation on the Hypersphere (PMH) is a power efficient modulation scheme for the \textit{load-modulated} multiple-input multiple-output (MIMO) transmitters with central power amplifiers (CPA). However, it is difficult to obtain the precise channel state information (CSI), and the traditional optimal maximum lik…

In this paper, we present new results on using orthogonal matching pursuit (OMP), to solve the sparse approximation problem over redundant dictionaries for complex cases (i.e., complex measurement vector, complex dictionary and complex additive white Gaussian noise (CAWGN)). A sufficient condition that OMP can recover …

Improves signal detection in non-Gaussian noise using transformed data.

VDA improves disentanglement of latent representations in complex signals.

In sparse Bayesian learning (SBL), Gaussian scale mixtures (GSMs) have been used to model sparsity-inducing priors that realize a class of concave penalty functions for the regression task in real-valued signal models. Motivated by the relative scarcity of formal tools for SBL in complex-valued models, this paper propo…

Paper proposes efficient methods for clustering and signal recovery in high-dimensional data with block structures.

Study on estimating signals from shifted and noisy copies in high dimensions, revealing a phase transition.