Noise Amplification Factor Research Articles

Consistency of MODIS surface bidirectional reflectance distribution function and albedo retrievals: 1. Algorithm performance

The first consistent year (November 2000 to November 2001) of global albedo product was produced at 1‐km resolution every 16 days from the observations of the Moderate‐Resolution Imaging Spectroradiometer (MODIS) instrument aboard NASA's Terra spacecraft. We evaluated the quality of the operational albedo retrievals in two ways: (1) by examining the algorithm performance using the product quality assurance (QA) fields (this paper) and (2) by comparing retrieved albedos with those observed at ground stations and by other satellite instruments (in a companion paper). The internal diagnostics of the retrieval algorithm adequately reflect the goodness of the model fit and the random noise amplification in the retrieved albedo. Global QA statistics show that the RossThick‐LiSparse‐Reciprocal model fits the atmospherically corrected surface reflectances very well, and the random noise amplification factors for white sky albedo and reflectance are generally less than 1.0. Cloud obscuration is the main reason for the activation of the backup magnitude retrieval algorithm. Over the 60°S to 60°N latitude band, 50% of the land pixels acquire more than six clear looks during 14–29 September 2001, and only 5% of these pixels are inverted with the backup algorithm. The latitude dependence and temporal distribution of the QA fields further demonstrate that the retrieval status mainly follows the pattern of angular sampling determined by cloud climatology and the instrument/orbit characteristics. A case study over the west coast of the United States shows that white sky shortwave albedos retrieved from magnitude inversions agree on average with those from full inversions to within 0.033 in reflectance units and have a slightly lower bias ranging from 0.014 to 0.023. We also explored the effect of residual cloud and aerosol contamination in the atmospherically corrected surface reflectance inputs in another case study over southern Africa. The quality assurance procedure of the operational MODIS bidirectional reflectance distribution function and albedo algorithm compensates for some of these residual effects and improves the albedo retrieval results by an order of 0.005 (10%) in the visible for more than 12% of pixels.

Design of a SENSE‐optimized high‐sensitivity MRI receive coil for brain imaging

An 8-channel receive-only detector array was developed for SENSE MRI of human brain. The coil geometry was based on a gapped element design and used ultra-high impedance preamplifiers for mutual decoupling of the elements. Computer simulations of the electric and magnetic fields showed that excellent signal-to-noise ratio (SNR) and SENSE performance could be achieved by placing the coil elements close to the head and maintaining a substantial gap between the elements. Measurements with a 1.5 T prototype coil showed a 2.7-fold improvement of the SNR averaged over the brain compared to a conventional quadrature birdcage receive coil and an average geometrical noise amplification factor (g-value) of 1.06 and 1.38 for rate-2 and rate-3 SENSE, respectively.

Prebifurcational noise rise in nonlinear systems

The phenomenon of prebifurcational noise increase in nonlinear systems in the process of period-doubling bifurcation is investigated. The study is conducted for a discrete system (quadratic mapping); how-ever, many of the laws discovered apply to more general systems. Estimates of the fluctuation variance are obtained both for the linear (away from the bifurcation threshold) and for the nonlinear mode (in the vicinity of the bifurcation threshold). It is shown that the variance of forced fluctuations in the strongly nonlinear mode is proportional to the root-mean-square of the noise intensity rather than to the variance. The possibility of measuring the noise in nonlinear systems on the basis of the prebifurcational noise amplification factor is demonstrated.

Vector sampling expansion

The vector sampling expansion (VSE) is an extension of Papoulis' (1977) generalized sampling expansion (GSE) to the vector case. In VSE, N bandlimited signals, all with the same bandwidth B, are passed through a multi-input-multi-output (MIMO) linear time invariant system that generates M (M/spl ges/N) output signals. The goal is to reconstruct the input signals from the samples of the output signals at a total sampling rate of N times the Nyquist rate, where the Nyquist rate is B//spl pi/ samples per second. We find necessary and sufficient conditions for this reconstruction. A surprising necessary condition for the case where all output signals are uniformly sampled at the same rate (N/M times the Nyquist rate) is that the expansion factor M/N must be an integer. This condition is no longer necessary when each output signal is sampled at a different rate or sampled nonuniformly. This work also includes a noise sensitivity analysis of VSE systems. We define the noise amplification factor, which allows a quantitative comparison between VSE systems, and determine the optimal VSE systems.

Theoretical noise sensitivity of BRDF and albedo retrieval from the EOS-MODIS and MISR sensors with respect to angular sampling

The sensitivity of the semiempirical RossThick-LiSparse Ambrals BRDF model to random noise in observed multiangular reflectances was investigated through a study of the impact of angular sampling. The mathematical properties of (linear, additive) kernel-driven BRDF models allow the analytical derivation of so-called weights of determination or noise amplification factors which quantify the uncertainty in retrieved parameters such as nadir-view reflectance or albedo at various solar zenith angles, or in the BRDF model parameters themselves. The study was carried out using simulated angular sampling for the MODIS and MISR instruments to be flown on NASA's Earth Observing System AM-1 platform, as a function of latitude, day of year and sampling period. A similar study was carried out for comparison using the modified RPV BRDF model, a multiplicative model. Results show that the retrieved parameters, reflectance and albedo can be expected to have noise amplification factors that are less than unity, indicating that the retrievals are stable with respect to random noise under the angular sampling schemes occurring. The BRDF model parameters themselves were found to be more susceptible to noise than many of the derived products, especially for the modified RPV model. The effect of different angular sampling regimes on the uncertainty of derived information was further explored. This study provides an indication of the reliability to be expected from the operational BRDF/albedo products from the MODIS and MISR instruments. The findings may qualitatively also apply to AVHRR, SPOT VEGETATION and similar satellite angular sampling regimes.

Constant modulus receivers under reduced noise amplification objective

A family of algorithms is presented for the adaptation of a fractionally spaced FIR channel equaliser for binary data. These algorithms incorporate an additive adjustment to the standard constant modulus objective so as to facilitate a reduction in the noise amplification factor. The novel algorithms essentially seek to balance the constant modulus objective of the equalisation with the noise power present in the output. The consequence of such a balance is that many of the local minima are excluded implicitly as, at those points, the noise amplification factor is greater than its value at the global minimum. Thus it is expected that a solution near the global minimum is likely to be attained. Computationally, these algorithms are of the same order as the standard CMA algorithm. Results support the expected behaviour of the algorithm.

The inverse problem of electrocardiology: the performance of inversion techniques as a function of patient anatomy.

Sixteen anatomically correct bodies have been studied to determine the performance of the inversion techniques of zero-order Tikhonov regularization and singular value decomposition. The bodies have varying heart height and diameter, thickness of subcutaneous fat layer, and distance of the heart from the left wall of the chest. Comparisons are made in terms of trade-off curves for noise amplification factor and spread of epicardial potentials. It was found that regularization performs better than singular value decomposition on all bodies; the larger the heart size, the more reliable the results; and for a given heart size, the thinner the subcutaneous fat layer, the more reliable the results. The distance of the heart from left wall of the chest was found to be a less significant factor for a given heart size.