White noise

About: White noise is a research topic. Over the lifetime, 16496 publications have been published within this topic receiving 318633 citations.

Wavelet Analysis and Synthesis of Stationary Long-Memory Processes

Abstract: The discrete wavelet transform (DWT) can be interpreted as a filtering of a time series by a set of octave band filters such that the width of each band as a proportion of its center frequency is constant. A long-memory process having a power spectrum that plots as a straight line on log-frequency/log-power scales over many octaves of frequency is intrinsically related to such a structure. As an example of such processes, we focus on one class of discrete-time, stationary, long-memory processes, the fractionally differenced Gaussian white noise processes (fdGn). We show how the DWT breaks down a fdGn, and show the exact correlation structure of the resulting coefficients for different wavelets (Daubechies' minimum-phase and least-asymmetric and Haar). The DWT is an impressive “whitening filter.” A discrete wavelet-based scheme for simulating fdGn's is discussed and is shown to be equivalent to a spectral decomposition of the covariance matrix of the process; however, it can be carried out using o...

Efficient detection in hyperspectral imagery

Abstract: Hyperspectral sensors collect hundreds of narrow and contiguously spaced spectral bands of data. Such sensors provide fully registered high resolution spatial and spectral images that are invaluable in discriminating between man-made objects and natural clutter backgrounds. The price paid for this high resolution data is extremely large data sets, several hundred of Mbytes for a single scene, that make storage and transmission difficult, thus requiring fast onboard processing techniques to reduce the data being transmitted. Attempts to apply traditional maximum likelihood detection techniques for in-flight processing of these massive amounts of hyperspectral data suffer from two limitations: first, they neglect the spatial correlation of the clutter by treating it as spatially white noise; second, their computational cost renders them prohibitive without significant data reduction like by grouping the spectral bands into clusters, with a consequent loss of spectral resolution. This paper presents a maximum likelihood detector that successfully confronts both problems: rather than ignoring the spatial and spectral correlations, our detector exploits them to its advantage; and it is computationally expedient, its complexity increasing only linearly with the number of spectral bands available. Our approach is based on a Gauss-Markov random field (GMRF) modeling of the clutter, which has the advantage of providing a direct parameterization of the inverse of the clutter covariance, the quantity of interest in the test statistic. We discuss in detail two alternative GMRF detectors: one based on a binary hypothesis approach, and the other on a "single" hypothesis formulation. We analyze extensively with real hyperspectral imagery data (HYDICE and SEBASS) the performance of the detectors, comparing them to a benchmark detector, the RX-algorithm. Our results show that the GMRF "single" hypothesis detector outperforms significantly in computational cost the RX-algorithm, while delivering noticeable detection performance improvement.

Characterization and prediction of gradient acoustic noise in MR imagers.

Abstract: Gradient acoustic noise has been measured and characterized for an epoxy-potted, shielded gradient assembly in a 1.5 T MRI system. Noise levels vary by 10 dB or more as a function of longitudinal position in the scanner and reflect the pattern of forces applied to the gradient assembly. The noise level increases slightly (1-3 dB) with a patient in the scanner. The spectrum of the noise is similar (but not identical) to the spectrum of the input signal. A gradient-pulse-to-acoustic-noise transfer function was obtained by using a white noise voltage input to the gradient system. The transfer function enabled us to accurately predict acoustic noise output for a pulse sequence consisting of a series of trapezoidal pulses on a single axis and for a clinical fast spin echo sequence with gradients present on all three axes.

The Output Distribution of Median Type Filters

Abstract: The distribution of the output of the one-dimensional median filter is derived for several cases including the k th-order output distribution with any input distribution. This is then used in several illustrative examples of median filtering a signal plus white noise.

The Generalized Cell Mapping Method in Nonlinear Random Vibration Based Upon Short-Time Gaussian Approximation

Abstract: This scheme provides a very efficient and accurate way of computing the one-step transition probability matrix of the previously developed generalized cell mapping (GCM) method in nonlinear random vibration