51,527 research outputs found
Estimation of signal-to-noise ratios
Statistical method estimates signal-to-noise ratios in an observed random voltage, such as the output of a telemetry receiver. Signals from a distant transmitting source, overlaid by noise signals, are monitored continuously
Adaptive estimation of High-Dimensional Signal-to-Noise Ratios
We consider the equivalent problems of estimating the residual variance, the
proportion of explained variance and the signal strength in a
high-dimensional linear regression model with Gaussian random design. Our aim
is to understand the impact of not knowing the sparsity of the regression
parameter and not knowing the distribution of the design on minimax estimation
rates of . Depending on the sparsity of the regression parameter,
optimal estimators of either rely on estimating the regression parameter
or are based on U-type statistics, and have minimax rates depending on . In
the important situation where is unknown, we build an adaptive procedure
whose convergence rate simultaneously achieves the minimax risk over all up
to a logarithmic loss which we prove to be non avoidable. Finally, the
knowledge of the design distribution is shown to play a critical role. When the
distribution of the design is unknown, consistent estimation of explained
variance is indeed possible in much narrower regimes than for known design
distribution
DTI denoising for data with low signal to noise ratios
Low signal to noise ratio (SNR) experiments in diffusion tensor imaging (DTI) give key information about tracking and anisotropy, e. g., by measurements with small voxel sizes or with high b values. However, due to the complicated and dominating impact of thermal noise such data are still seldom analysed. In this paper Monte Carlo simulations are presented which investigate the distributions of noise for different DTI variables in low SNR situations. Based on this study a strategy for the application of spatial smoothing is derived. Optimal prerequisites for spatial filters are unbiased, bell shaped distributions with uniform variance, but, only few variables have a statistics close to that. To construct a convenient filter a chain of nonlinear Gaussian filters is adapted to peculiarities of DTI and a bias correction is introduced. This edge preserving three dimensional filter is then validated via a quasi realistic model. Further, it is shown that for small sample sizes the filter is as effective as a maximum likelihood estimator and produces reliable results down to a local SNR of approximately 1. The filter is finally applied to very recent data with isotropic voxels of the size 1Ć1Ć1mm^3 which corresponds to a spatially mean SNR of 2.5. This application demonstrates the statistical robustness of the filter method. Though the Rician noise model is only approximately realized in the data, the gain of information by spatial smoothing is considerable
Outage Capacity of Incremental Relaying at Low Signal-to-Noise Ratios
We present the \epsilon-outage capacity of incremental relaying at low
signal-to-noise ratios (SNR) in a wireless cooperative network with slow
Rayleigh fading channels. The relay performs decode-and-forward and repetition
coding is employed in the network, which is optimal in the low SNR regime. We
derive an expression on the optimal relay location that maximizes the
\epsilon-outage capacity. It is shown that this location is independent of the
outage probability and SNR but only depends on the channel conditions
represented by a path-loss factor. We compare our results to the
\epsilon-outage capacity of the cut-set bound and demonstrate that the ratio
between the \epsilon-outage capacity of incremental relaying and the cut-set
bound lies within 1/\sqrt{2} and 1. Furthermore, we derive lower bounds on the
\epsilon-outage capacity for the case of K relays.Comment: 5 pages, 4 figures, to be presented at VTC Fall 2009 in Anchorage,
Alask
Performance of binary block codes at low signal-to-noise ratios
The performance of general binary block codes on an unquantized additive white Gaussian noise (AWGN) channel at low signal-to-noise ratios is considered. Expressions are derived for both the block error and the bit error probabilities near the point where the bit signal-to-noise ratio is zero. These expressions depend on the global geometric structure of the code, although the minimum distance still seems to play a crucial role. Examples of codes such as orthogonal codes, biorthogonal codes, the (24,12) extended Golay code, and the (15,6) expurgated BCH code are discussed. The asymptotic coding gain at low signal-to-noise ratios is also studied
Spatial Smoothing for Diffusion Tensor Imaging with low Signal to Noise Ratios
Though low signal to noise ratio (SNR) experiments in DTI give key information about tracking and anisotropy, e.g. by measurements with very small voxel sizes, due to the complicated impact of thermal noise such experiments are up to now seldom analysed. In this paper Monte Carlo simulations are presented which investigate the random fields of noise for different DTI variables in low SNR situations. Based on this study a strategy for spatial smoothing, which demands essentially uniform noise, is derived. To construct a convenient filter the weights of the nonlinear Aurich chain are adapted to DTI. This edge preserving three dimensional filter is then validated in different variants via a quasi realistic model and is applied to very new data with isotropic voxels of the size 1x1x1 mm3 which correspond to a spatial mean SNR of approximately 3
Signal-to-noise ratio for the wide field-planetary camera of the Space Telescope
Signal-to-noise ratios for the Wide Field Camera and Planetary Camera of the Space Telescope were calculated as a function of integration time. Models of the optical systems and CCD detector arrays were used with a 27th visual magnitude point source and a 25th visual magnitude per arc-sq. second extended source. A 23rd visual magnitude per arc-sq. second background was assumed. The models predicted signal-to-noise ratios of 10 within 4 hours for the point source centered on a signal pixel. Signal-to-noise ratios approaching 10 are estimated for approximately 0.25 x 0.25 arc-second areas within the extended source after 10 hours integration
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