4,242 research outputs found
Extended object reconstruction in adaptive-optics imaging: the multiresolution approach
We propose the application of multiresolution transforms, such as wavelets
(WT) and curvelets (CT), to the reconstruction of images of extended objects
that have been acquired with adaptive optics (AO) systems. Such multichannel
approaches normally make use of probabilistic tools in order to distinguish
significant structures from noise and reconstruction residuals. Furthermore, we
aim to check the historical assumption that image-reconstruction algorithms
using static PSFs are not suitable for AO imaging. We convolve an image of
Saturn taken with the Hubble Space Telescope (HST) with AO PSFs from the 5-m
Hale telescope at the Palomar Observatory and add both shot and readout noise.
Subsequently, we apply different approaches to the blurred and noisy data in
order to recover the original object. The approaches include multi-frame blind
deconvolution (with the algorithm IDAC), myopic deconvolution with
regularization (with MISTRAL) and wavelets- or curvelets-based static PSF
deconvolution (AWMLE and ACMLE algorithms). We used the mean squared error
(MSE) and the structural similarity index (SSIM) to compare the results. We
discuss the strengths and weaknesses of the two metrics. We found that CT
produces better results than WT, as measured in terms of MSE and SSIM.
Multichannel deconvolution with a static PSF produces results which are
generally better than the results obtained with the myopic/blind approaches
(for the images we tested) thus showing that the ability of a method to
suppress the noise and to track the underlying iterative process is just as
critical as the capability of the myopic/blind approaches to update the PSF.Comment: In revision in Astronomy & Astrophysics. 19 pages, 13 figure
Detection of hidden structures on all scales in amorphous materials and complex physical systems: basic notions and applications to networks, lattice systems, and glasses
Recent decades have seen the discovery of numerous complex materials. At the
root of the complexity underlying many of these materials lies a large number
of possible contending atomic- and larger-scale configurations and the
intricate correlations between their constituents. For a detailed
understanding, there is a need for tools that enable the detection of pertinent
structures on all spatial and temporal scales. Towards this end, we suggest a
new method by invoking ideas from network analysis and information theory. Our
method efficiently identifies basic unit cells and topological defects in
systems with low disorder and may analyze general amorphous structures to
identify candidate natural structures where a clear definition of order is
lacking. This general unbiased detection of physical structure does not require
a guess as to which of the system properties should be deemed as important and
may constitute a natural point of departure for further analysis. The method
applies to both static and dynamic systems.Comment: (23 pages, 9 figures
A Scale-Separated Dynamic Mode Decomposition From Observations of the Ionospheric Electron Density Profile
We present a method for modeling a time series of ionospheric electron
density profiles using modal decompositions. Our method is based on the Dynamic
Mode Decomposition (DMD), which provides a means of determining spatiotemporal
modes from measurements alone. DMD-derived models can be easily updated as new
data is recorded and do not require any physics to inform the dynamics.
However, in the case of ionospheric profiles, we find a wide range of
oscillations, including some far above the diurnal frequency. Therefore, we
propose nontrivial extensions to DMD using multiresolution analysis (MRA) via
wavelet decompositions. We call this method the Scale-Separated Dynamic Mode
Decomposition (SSDMD) since the MRA isolates fluctuations at different scales
within the time series into separated components. We show that this method
provides a stable reconstruction of the mean plasma density and can be used to
predict the state of the vertical profile at future time steps. We demonstrate
the SSDMD method on data sets covering periods of high and low solar activity.Comment: 26 pages, 16 figure
A black-box model for neurons
We explore the identification of neuronal voltage traces by artificial neural networks based on wavelets (Wavenet). More precisely, we apply a modification in the representation of dynamical systems by Wavenet which decreases the number of used functions; this approach combines localized and global scope functions (unlike Wavenet, which uses localized functions only). As a proof-of-concept, we focus on the identification of voltage traces obtained by simulation of a paradigmatic neuron model, the Morris-Lecar model. We show that, after training our artificial network with biologically plausible input currents, the network is able to identify the neuron's behaviour with high accuracy, thus obtaining a black box that can be then used for predictive goals. Interestingly, the interval of input currents used for training, ranging from stimuli for which the neuron is quiescent to stimuli that elicit spikes, shows the ability of our network to identify abrupt changes in the bifurcation diagram, from almost linear input-output relationships to highly nonlinear ones. These findings open new avenues to investigate the identification of other neuron models and to provide heuristic models for real neurons by stimulating them in closed-loop experiments, that is, using the dynamic-clamp, a well-known electrophysiology technique.Peer ReviewedPostprint (author's final draft
Information Surfaces in Systems Biology and Applications to Engineering Sustainable Agriculture
Systems biology of plants offers myriad opportunities and many challenges in
modeling. A number of technical challenges stem from paucity of computational
methods for discovery of the most fundamental properties of complex dynamical
systems. In systems engineering, eigen-mode analysis have proved to be a
powerful approach. Following this philosophy, we introduce a new theory that
has the benefits of eigen-mode analysis, while it allows investigation of
complex dynamics prior to estimation of optimal scales and resolutions.
Information Surfaces organizes the many intricate relationships among
"eigen-modes" of gene networks at multiple scales and via an adaptable
multi-resolution analytic approach that permits discovery of the appropriate
scale and resolution for discovery of functions of genes in the model plant
Arabidopsis. Applications are many, and some pertain developments of crops that
sustainable agriculture requires.Comment: 24 Pages, DoCEIS 1
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