Signal-to-noise ratio of Gaussian-state ghost imaging

The signal-to-noise ratios (SNRs) of three Gaussian-state ghost imaging configurations--distinguished by the nature of their light sources--are derived. Two use classical-state light, specifically a joint signal-reference field state that has either the maximum phase-insensitive or the maximum phase-sensitive cross correlation consistent with having a proper $P$ representation. The third uses nonclassical light, in particular an entangled signal-reference field state with the maximum phase-sensitive cross correlation permitted by quantum mechanics. Analytic SNR expressions are developed for the near-field and far-field regimes, within which simple asymptotic approximations are presented for low-brightness and high-brightness sources. A high-brightness thermal-state (classical phase-insensitive state) source will typically achieve a higher SNR than a biphoton-state (low-brightness, low-flux limit of the entangled-state) source, when all other system parameters are equal for the two systems. With high efficiency photon-number resolving detectors, a low-brightness, high-flux entangled-state source may achieve a higher SNR than that obtained with a high-brightness thermal-state source.Comment: 12 pages, 4 figures. This version incorporates additional references and a new analysis of the nonclassical case that, for the first time, includes the complete transition to the classical signal-to-noise ratio asymptote at high source brightnes

Signal-to-Noise Ratio in Squeezed-Light Laser Radar

The formalism for computing the signal-to-noise ratio (SNR) for laser radar is reviewed and applied to the tasks of target detection, direction-finding, and phase change estimation with squeezed light. The SNR for heterodyne detection of coherent light using a squeezed local oscillator is lower than that obtained using a coherent local oscillator. This is true for target detection, for phase estimation, and for direction-finding with a split detector. Squeezing the local oscillator also lowers SNR in balanced homodyne and heterodyne detection of coherent light. Loss places an upper bound on the improvement that squeezing can bring to direct-detection SNR.Comment: Typos correcte

Signal to noise ratio analysis in virtual source array imaging

We consider correlation-based imaging of a reflector located on one side of a passive array where the medium is homogeneous. On the other side of the array the illumination by remote impulsive sources goes through a strongly scattering medium. It has been shown in [J. Garnier and G. Papanicolaou, Inverse Problems 28 (2012), 075002] that migrating the cross correlations of the passive array gives an image whose resolution is as good as if the array was active and the array response matrix was that of a homogeneous medium. In this paper we study the signal to noise ratio of the image as a function of statistical properties of the strongly scattering medium, the signal bandwidth and the source and passive receiver array characteristics. Using a Kronecker model for the strongly scattering medium we show that image resolution is as expected and that the signal to noise ratio can be computed in an essentially explicit way. We show with direct numerical simulations using full wave propagation solvers in random media that the theoretical predictions based on the Kronecker model are accurate

Sequential joint signal detection and signal-to-noise ratio estimation

The sequential analysis of the problem of joint signal detection and signal-to-noise ratio (SNR) estimation for a linear Gaussian observation model is considered. The problem is posed as an optimization setup where the goal is to minimize the number of samples required to achieve the desired (i) type I and type II error probabilities and (ii) mean squared error performance. This optimization problem is reduced to a more tractable formulation by transforming the observed signal and noise sequences to a single sequence of Bernoulli random variables; joint detection and estimation is then performed on the Bernoulli sequence. This transformation renders the problem easily solvable, and results in a computationally simpler sufficient statistic compared to the one based on the (untransformed) observation sequences. Experimental results demonstrate the advantages of the proposed method, making it feasible for applications having strict constraints on data storage and computation.Comment: 5 pages, Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), 201

Estimating the signal-to-noise ratio of AVIRIS data

To make the best use of narrowband airborne visible/infrared imaging spectrometer (AVIRIS) data, an investigator needs to know the ratio of signal to random variability or noise (signal-to-noise ratio or SNR). The signal is land cover dependent and varies with both wavelength and atmospheric absorption; random noise comprises sensor noise and intrapixel variability (i.e., variability within a pixel). The three existing methods for estimating the SNR are inadequate, since typical laboratory methods inflate while dark current and image methods deflate the SNR. A new procedure is proposed called the geostatistical method. It is based on the removal of periodic noise by notch filtering in the frequency domain and the isolation of sensor noise and intrapixel variability using the semi-variogram. This procedure was applied easily and successfully to five sets of AVIRIS data from the 1987 flying season and could be applied to remotely sensed data from broadband sensors

Signal to Noise Ratio estimation in passive correlation-based imaging

We consider imaging with passive arrays of sensors using as illumination ambient noise sources. The first step for imaging under such circumstances is the computation of the cross correlations of the recorded signals, which have attracted a lot of attention recently because of their numerous applications in seismic imaging, volcano monitoring, and petroleum prospecting. Here, we use these cross correlations for imaging reflectors with travel-time migration. While the resolution of the image obtained this way has been studied in detail, an analysis of the signal-to-noise ratio (SNR) is presented in this paper along with numerical simulations that support the theoretical results. It is shown that the SNR of the image inherits the SNR of the computed cross correlations and therefore it is proportional to the square root of the bandwidth of the noise sources times the recording time. Moreover, the SNR of the image is proportional to the array size. This means that the image can be stabilized by increasing the size of the array when the recorded signals are not of long duration, which is important in applications such as non-destructive testing

Filter distortion effects on telemetry signal-to-noise ratio

The effect of filtering on the Signal-to-Noise Ratio (SNR) of a coherently demodulated band-limited signal is determined in the presence of worse-case amplitude ripple. The problem is formulated mathematically as an optimization problem in the L2-Hilbert space. The form of the worst-cast amplitude ripple is specified, and the degradation in the SNR is derived in a closed form expression. It is shown that when the maximum passband amplitude ripple is 2 delta (peak to peak), the SNR is degraded by at most (1 - delta squared), even when the ripple is unknown or uncompensated. For example, an SNR loss of less than 0.01 dB due to amplitude ripple can be assured by keeping the amplitude ripple to under 0.42 dB