2,481 research outputs found
Intermittent process analysis with scattering moments
Scattering moments provide nonparametric models of random processes with
stationary increments. They are expected values of random variables computed
with a nonexpansive operator, obtained by iteratively applying wavelet
transforms and modulus nonlinearities, which preserves the variance. First- and
second-order scattering moments are shown to characterize intermittency and
self-similarity properties of multiscale processes. Scattering moments of
Poisson processes, fractional Brownian motions, L\'{e}vy processes and
multifractal random walks are shown to have characteristic decay. The
Generalized Method of Simulated Moments is applied to scattering moments to
estimate data generating models. Numerical applications are shown on financial
time-series and on energy dissipation of turbulent flows.Comment: Published in at http://dx.doi.org/10.1214/14-AOS1276 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Intelligent non-cooperative optical networks: Leveraging scattering neural networks with small training data
\ua9 2024 The Author(s)Artificial intelligence (AI) is enabling intelligent communications where learning based signal classification simplifies optical network signal allocation and shifts signal processing pressure to each network edge. This work proposes a non-orthogonal signal waveform framework that leverages its unique spectral compression characteristic as a user address for efficiently forwarding messages to target users. The primary focus of this work lies in the physical layer intelligent receiver design, which can automatically identify different received signal formats without preamble notification in a non-cooperative communication approach. Traditional signal classification methods, such as convolutional neural network (CNN), rely on extensive training, resulting in a heavy dependency on large training datasets. To overcome this limitation, this work designs a specific two-layer scattering neural network that can accurately separate signals even when the training data is limited, leading to reduced training complexity. Its performance remains robust in diverse transmission conditions. Furthermore, the scattering neural network is interpretable because features are extracted based on deterministic wavelet filters rather than training based filters
Modeling Land-Cover Types Using Multiple Endmember Spectral Mixture Analysis in a Desert City
Spectral mixture analysis is probably the most commonly used approach among sub-pixel analysis techniques. This method models pixel spectra as a linear combination of spectral signatures from two or more ground components. However, spectral mixture analysis does not account for the absence of one of the surface features or spectral variation within pure materials since it utilizes an invariable set of surface features. Multiple endmember spectral mixture analysis (MESMA), which addresses these issues by allowing endmembers to vary on a per pixel basis, was employed in this study to model Landsat ETM+ reflectance in the Phoenix metropolitan area. Image endmember spectra of vegetation, soils, and impervious surfaces were collected with the use of a fine resolution Quickbird image and the pixel purity index. This study employed 204 (=3x17x4) total four-endmember models for the urban subset and 96 (=6x6x2x4) total five-endmember models for the non-urban subset to identify fractions of soil, impervious surface, vegetation, and shade. The Pearson correlation between the fraction outputs from MESMA and reference data from Quickbird 60 cm resolution data for soil, impervious, and vegetation were 0.8030, 0.8632, and 0.8496 respectively. Results from this study suggest that the MESMA approach is effective in mapping urban land covers in desert cities at sub- pixel level.
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Tissue multifractality and Born approximation in analysis of light scattering: a novel approach for precancers detection
Multifractal, a special class of complex self-affine processes, are under recent intensive investigations because of their fundamental nature and potential applications in diverse physical systems. Here, we report on a novel light scattering-based inverse method for extraction/quantification of multifractality in the spatial distribution of refractive index of biological tissues. The method is based on Fourier domain pre-processing via the Born approximation, followed by the Multifractal Detrended Fluctuation Analysis. The approach is experimentally validated in synthetic multifractal scattering phantoms, and tested on biopsy tissue slices. The derived multifractal properties appear sensitive in detecting cervical precancerous alterations through an increase of multifractality with pathology progression, demonstrating the potential of the developed methodology for novel precancer biomarker identification and tissue diagnostic tool. The novel ability to delineate the multifractal optical properties from light scattering signals may also prove useful for characterizing a wide variety of complex scattering media of non-biological origin
Hyperspectral Unmixing Overview: Geometrical, Statistical, and Sparse Regression-Based Approaches
Imaging spectrometers measure electromagnetic energy scattered in their
instantaneous field view in hundreds or thousands of spectral channels with
higher spectral resolution than multispectral cameras. Imaging spectrometers
are therefore often referred to as hyperspectral cameras (HSCs). Higher
spectral resolution enables material identification via spectroscopic analysis,
which facilitates countless applications that require identifying materials in
scenarios unsuitable for classical spectroscopic analysis. Due to low spatial
resolution of HSCs, microscopic material mixing, and multiple scattering,
spectra measured by HSCs are mixtures of spectra of materials in a scene. Thus,
accurate estimation requires unmixing. Pixels are assumed to be mixtures of a
few materials, called endmembers. Unmixing involves estimating all or some of:
the number of endmembers, their spectral signatures, and their abundances at
each pixel. Unmixing is a challenging, ill-posed inverse problem because of
model inaccuracies, observation noise, environmental conditions, endmember
variability, and data set size. Researchers have devised and investigated many
models searching for robust, stable, tractable, and accurate unmixing
algorithms. This paper presents an overview of unmixing methods from the time
of Keshava and Mustard's unmixing tutorial [1] to the present. Mixing models
are first discussed. Signal-subspace, geometrical, statistical, sparsity-based,
and spatial-contextual unmixing algorithms are described. Mathematical problems
and potential solutions are described. Algorithm characteristics are
illustrated experimentally.Comment: This work has been accepted for publication in IEEE Journal of
Selected Topics in Applied Earth Observations and Remote Sensin
Scale Dependencies and Self-Similarity Through Wavelet Scattering Covariance
We introduce a scattering covariance matrix which provides non-Gaussian
models of time-series having stationary increments. A complex wavelet transform
computes signal variations at each scale. Dependencies across scales are
captured by the joint covariance across time and scales of complex wavelet
coefficients and their modulus. This covariance is nearly diagonalized by a
second wavelet transform, which defines the scattering covariance. We show that
this set of moments characterizes a wide range of non-Gaussian properties of
multi-scale processes. This is analyzed for a variety of processes, including
fractional Brownian motions, Poisson, multifractal random walks and Hawkes
processes. We prove that self-similar processes have a scattering covariance
matrix which is scale invariant. This property can be estimated numerically and
defines a class of wide-sense self-similar processes. We build maximum entropy
models conditioned by scattering covariance coefficients, and generate new
time-series with a microcanonical sampling algorithm. Applications are shown
for highly non-Gaussian financial and turbulence time-series
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