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Regularizing the least-squares criterion with the total number of coefficient changes, it is possible to estimate time-varying (TV) autoregressive (AR) models with piecewise-constant coefficients. Such models emerge in various applications including speech segmentation using linear predictors. To cope with the large-size optimization task, the problem is cast as a sparse regression one, and is solved...
We present a method for optimization with sums of exponentials subject to positivity constraints and apply it to the modeling of empirical probability distribution functions and to the design of IIR filters with non-negative impulse response. Our approach uses exponents in a sparse arithmetic progression and hence is able to transform the positivity condition to a polynomial form that is computationally...
In this paper, a new coding scheme for the multiple access channel (MAC) with noisy cooperative links is proposed. The cooperation cost is modelled by powers spent on exchanging common information at transmitters. The optimal power allocation policy is derived to explore the tradeoff between cooperation and transmission. For some important cases, optimal power allocation that maximizes weighted sum...
One of the early successful approaches to deal with the now classical ℓ2 + ℓ1 optimization formulation of sparse signal recovery (often known as the LASSO) was based on re-writing it as a bound-constrained quadratic program (BCQP), which was then tackled using a gradient projection (GP) algorithm with a spectral (Barzilai-Borwein) step choice. The resulting algorithm (called gradient projection for...
Consider a wireless scenario in which a multi-antenna transmitter wants to send a confidential message to a single-antenna information receiver (IR) while transferring wireless energy to a number of multi-antenna energy receivers (ERs). In order to keep the ERs from retrieving the confidential message, an artificial noise (AN)-aided physical-layer secrecy approach is employed at the transmitter. The...
We propose a new algorithm to efficiently obtain non-negative sparse representations for audio. The spectrum of an audio signal is represented as a sparse linear combination of atoms taken from an overcomplete dictionary. The algorithm is based on minimizing the generalized Kullback-Leibler divergence between an observed magnitude spectrum and a non-negative linear combination of atoms, plus an ℓ1...
Transmission power variance constrained power allocation in single carrier multiuser (MU) single-input multiple-output (SIMO) systems with iterative frequency domain (FD) soft cancelation (SC) minimum mean squared error (MMSE) equalization is considered in this paper. It is known in the literature that peak to average power ratio (PAPR) at the transmitter can be decreased by reducing the variance...
In this paper, we consider the problem of estimating a spatially varying field in a wireless sensor network, where resource constraints limit the number of sensors selected in the network that provide their measurements for field estimation. Based on a one-to-one correspondence between the selected sensors and the nonzero elements of Kriging weights, we propose a sparsity-promoting ordinary Kriging...
In this paper, we propose a novel method to estimate the fundamental frequencies and directions-of-arrival (DOA) of multi-pitch signals impinging on a sensor array. Formulating the estimation as a group sparse convex optimization problem, we use the alternating direction of multipliers method (ADMM) to estimate both temporal and spatial correlation of the array signal. By first jointly estimating...
Many real-world processes evolve in cascades over networks, whose topologies are often unobservable and change over time. However, the so-termed adoption times when for instance blogs mention popular news items are typically known, and are implicitly dependent on the underlying network. To infer the network topology, a dynamic structural equation model is adopted to capture the relationship between...
This paper deals with the recovery of an unknown, low-rank matrix from quantized and (possibly) corrupted measurements of a subset of its entries. We develop statistical models and corresponding (multi-)convex optimization algorithms for quantized matrix completion (Q-MC) and quantized robust principal component analysis (Q-RPCA). In order to take into account the quantized nature of the available...
Sensor selection is an important design task in sensor networks. We consider the problem of adaptive sensor selection for applications in which the observations follow a non-linear model, e.g., target/bearing tracking. In adaptive sensor selection, based on the dynamical state model and the state estimate from the previous time step, the most informative sensors are selected to acquire the measurements...
The problem of jammers suppression in colocated multiple-input multiple-output (MIMO) radar is considered. We resort to reduced dimension (RD) beamspace designs with robust-ness/adaptiveness to achieve the goal of efficient jammers suppression. Specifically, our RD beamspace techniques aim at designing optimal beamspace matrices based on reasonable tradeoffs between the desired in-sector source distortion...
This paper presents a 2D transposition of the Hilbert-Huang Transform (HHT), an empirical data analysis method designed for studying instantaneous amplitudes and phases of non-stationary data. The principle is to adaptively decompose an image into oscillating parts called Intrinsic Mode Functions (IMFs) using an Empirical Mode Decomposition method (EMD), and then to perform Hilbert spectral analysis...
In recent works, compressed sensing and convex optimization techniques have been applied to radio-interferometric imaging showing the potential to outperform state-of-the-art imaging algorithms in the field. We review our latest contributions, which leverage the versatility of convex optimization to both handle realistic continuous visibilities and offer a highly parallelizable structure paving the...
Optimal rate allocation is among the most challenging tasks to perform in the context of predictive video coding, because of the dependencies between frames induced by motion compensation. In this paper, we derive an analytical rate-distortion model that explicitly takes into account the dependencies between frames. The proposed approach allows us to formulate the frame-level optimal rate allocation...
In a large network of agents, we consider a distributed convex optimization problem where each agent has a private convex cost function and a set of local variables. We provide an algorithm to carry out a multi-area decentralized optimization in an asynchronous fashion, obtained by applying random Gauss-Seidel iterations on the Douglas-Rachford splitting operator. As an application, a direct-current...
The problem of finding clusters in a graph arises in several applications such as social networks, data mining and computer networks. A typical, convex optimization-approach, that is often adopted is to identify a sparse plus low-rank decomposition of the adjacency matrix of the graph, with the (dense) low-rank component representing the clusters. In this paper, we sharply characterize the conditions...
Sparsity inducing penalizations are useful tools in variational methods for machine learning. In this paper, we design a learning algorithm for multiclass support vector machines that allows us to enforce sparsity through various nonsmooth regularizations, such as the mixed ℓ1, p-norm with p ≥ 1. The proposed constrained convex optimization approach involves an epigraphical constraint for which we...
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