Aurele Balavoine

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We present an analysis of the Locally Competitive Algorithm (LCA), which is a Hopfield-style neural network that efficiently solves sparse approximation problems (e.g., approximating a vector from a dictionary using just a few nonzero coefficients). This class of problems plays a significant role in both theories of neural coding and applications in signal(More)
Analog circuits and systems research and education can benefit from the flexibility provided by large-scale Field Programmable Analog Arrays (FPAAs). This paper presents the hardware and software infrastructure supporting the use of a family of floating-gate based FPAAs being developed at Georgia Tech. This infrastructure is compact and portable and(More)
This paper studies the convergence rate of a continuous-time dynamical system for l<sub>1</sub>-minimization, known as the Locally Competitive Algorithm (LCA). Solving l<sub>1</sub>-minimization problems efficiently and rapidly is of great interest to the signal processing community, as these programs have been shown to recover sparse solutions to(More)
There exist many well-established techniques to recover sparse signals from compressed measurements with known performance guarantees in the static case. More recently, new methods have been proposed to tackle the recovery of time-varying signals, but few benefit from a theoretical analysis. In this paper, we give theoretical guarantees for the Iterative(More)
The Locally Competitive Algorithm (LCA) is a continuoustime dynamical system designed to solve the problem of sparse approximation. This class of approximation problems plays an important role in producing state-of-the-art results in many signal processing and inverse problems, and implementing the LCA in analog VLSI may significantly improve the time and(More)
There exist many well-established techniques to recover sparse signals from compressed measurements with known performance guarantees in the static case. However, only a few methods have been proposed to tackle the recovery of time-varying signals, and even fewer benefit from a theoretical analysis. In this paper, we study the capacity of the Iterative(More)
Despite the importance of sparsity signal models and the increasing prevalence of high-dimensional streaming data, there are relatively few algorithms for dynamic filtering of time-varying sparse signals. Of the existing algorithms, fewer still provide strong performance guarantees. This paper examines two algorithms for dynamic filtering of sparse signals(More)
Sparse approximation is an optimization program that produces state-of-the-art results in many applications in signal processing and engineering. To deploy this approach in real-time, it is necessary to develop faster solvers than are currently available in digital. The Locally Competitive Algorithm (LCA) is a dynamical system designed to solve the class of(More)
Compressed sensing is an important optimization problem in signal and image processing applications. A Hopfield-Network-like analog system is proposed as a solution, using the Locally Competitive Algorithm (LCA) [1] to solve an overcomplete l1 sparse approximation problem. A scalable system architecture using sub-threshold currents is described. A(More)
Recovering static signals from compressed measurements is an important problem that has been extensively studied in modern signal processing. However, only recently have methods been proposed to tackle the problem of recovering a time-varying sequence from streaming online compressed measurements. In this paper, we study the capacity of the standard(More)