Handling nonnegative constraints in spectral estimation

Alkire, Brien; Vandenberghe, Lieven

doi:10.1109/acssc.2000.910945

Cited by 12 publications

(2 citation statements)

References 4 publications

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“…A related problem is parameter estimation where we fit a model to data. One example of this is fitting MA or ARMA models; here parameter estimation can be carried out with convex optimization [51], [52], [53].…”

Section: B Signal Processing Via Convex Optimizationmentioning

confidence: 99%

Real-Time Convex Optimization in Signal Processing

Mattingley¹,

Boyd²

2010

IEEE Signal Process. Mag.

265

178

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Abstract-Convex optimization has been used in signal processing for a long time, to choose coefficients for use in fast (linear) algorithms, such as in filter or array design; more recently, it has been used to carry out (nonlinear) processing on the signal itself. Examples of the latter case include total variation de-noising, compressed sensing, fault detection, and image classification. In both scenarios, the optimization is carried out on time scales of seconds or minutes, and without strict time constraints. Convex optimization has traditionally been considered computationally expensive, so its use has been limited to applications where plenty of time is available. Such restrictions are no longer justified. The combination of dramatically increased computational power, modern algorithms, and new coding approaches has delivered an enormous speed increase, which makes it possible to solve modest-sized convex optimization problems on microsecond or millisecond time scales, and with strict deadlines. This enables real-time convex optimization in signal processing.

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Section: B Signal Processing Via Convex Optimizationmentioning

confidence: 99%

Real-Time Convex Optimization in Signal Processing

Mattingley¹,

Boyd²

2010

IEEE Signal Process. Mag.

265

178

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“…It is hard to analyze the case when parameter λ is smaller because in this case it is not clear how to construct u I c which is critical for tractable KKT analysis. The choice ofû in the Theorem 2 is motivated by the proof techniques used in [13] and the main idea of of proof is to show that u given by the theorem satisfies KKT conditions. And this can be achieved via concentration of measure argument.…”

Section: Remarkmentioning

confidence: 99%

Noisy filtered sparse processes: Reconstruction and compression

Zhao

Saligrama

2010

49th IEEE Conference on Decision and Control (CDC)

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In this paper we consider estimation and compression of filtered sparse processes. Specifically, the filtered sparse process is a signal x ∈ R n obtained by driving a k-sparse signal u ∈ R n through an arbitrary unknown stable discrete-linear time invariant system H of a known order. The signal x(t) is measured noisily. We consider estimation of x(t) from noisy measurements. We also consider compression of x(t) by means of random projections analogous to compressed sensing. For different cases including AR and MA systems we show that x can indeed be reconstructed from O(k log(n)) measurements. We develop a novel LP optimization algorithm and show that both the unknown filter H and the sparse input u can be reliably estimated.

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