Threshold Effects in Parameter Estimation From Compressed Data
| Autor: | Ali Pezeshki, Pooria Pakrooh, Louis L. Scharf |
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| Rok vydání: | 2016 |
| Předmět: |
FOS: Computer and information sciences
Computer Science - Information Theory Gaussian Multivariate normal distribution 02 engineering and technology 01 natural sciences 010104 statistics & probability symbols.namesake Statistics 0202 electrical engineering electronic engineering information engineering 0101 mathematics Electrical and Electronic Engineering Gaussian process Mathematics Noise measurement business.industry Estimation theory Information Theory (cs.IT) 010102 general mathematics Pattern recognition 020206 networking & telecommunications Covariance Sample mean and sample covariance Linear subspace Gaussian noise Signal Processing symbols Artificial intelligence business Algorithm Subspace topology Data compression Signal subspace |
| Zdroj: | GlobalSIP |
| ISSN: | 1941-0476 1053-587X |
| DOI: | 10.1109/tsp.2016.2521617 |
| Popis: | In this paper, we investigate threshold effects associated with the swapping of signal and noise subspaces in estimating signal parameters from compressed noisy data. The term threshold effect refers to a sharp departure of mean-squared error from the Cramer–Rao bound when the signal-to-noise ratio falls below a threshold SNR. In many cases, the threshold effect is caused by a subspace swap event, when the measured data (or its sample covariance) is better approximated by a subset of components of an orthogonal subspace than by the components of a signal subspace. We derive analytical lower bounds on the probability of a subspace swap in compressively measured noisy data in two canonical models: a first-order model and a second-order model. In the first-order model, the parameters to be estimated modulate the mean of a complex multivariate normal set of measurements. In the second-order model, the parameters modulate the covariance of complex multivariate measurements. In both cases, the probability bounds are tail probabilities of $F$ -distributions, and they apply to any linear compression scheme. These lower bounds guide our understanding of threshold effects and performance breakdowns for parameter estimation using compression. In particular, they can be used to quantify the increase in threshold SNR as a function of a compression ratio $C$ . We demonstrate numerically that this increase in threshold SNR is roughly $10\log_{10} \ C$ dB, which is consistent with the performance loss that one would expect when measurements in Gaussian noise are compressed by a factor $C$ . |
| Databáze: | OpenAIRE |
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