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Solar telescopes will never be able to resolve the smallest events at their intrinsic physical scales. Pixel signals recorded by SOHO/(CDS, EIT, SUMER), STEREO/SECCHI/ EUVI, TRACE, SDO/AIA, and even by the future Solar Orbiter EUI/HRI contain an inherent “spatial noise” since they represent an average of the solar signal present at subpixel scales. In this paper, we aim at investigating this spatial noise, and hopefully at extracting information from subpixel scales. Two paths are explored. We first combine a regularity analysis of a sequence of EIT images with an estimation of the relationship between mean and standard deviation, and we formulate a scenario for the evolution of the local signal-to-noise ratio (SNR) as the pixel size becomes smaller. Second, we use an elementary forward modeling to examine the relationship between nanoflare characteristics (such as area, duration, and intensity) and the global mean and standard deviation. We use theoretical distributions of nanoflare parameters as input to the forward model. A fine-grid image is generated as a random superposition of those pseudo-nanoflares. Coarser resolution images (simulating images acquired by a telescope) are obtained by rebinning and are used to compute the mean and standard deviation to be analyzed. Our results show that the local SNR decays more slowly in regions exhibiting irregularities than in smooth regions. [ABSTRACT FROM AUTHOR]

We reformulate various versions of infinitely divisible cascades proposed in the literature using stochastic equations. This approach sheds a new light on the differences and common points of several formulations that have been recently provided by several teams. In particular, we focus on the simplification occurring when the infinitely divisible noise at the heart of such model is stable: an independently scattered random measure becomes a stable stochastic integral. In the last section we discuss the D-dimensional generalization. [ABSTRACT FROM AUTHOR]

The framework of infinitely divisible scaling was first developed to analyse the statistical intermittency of turbulence in fluid dynamics. It also reveals a powerful tool to describe and model various situations including Internet traffic, financial time series, textures ... A series of recent works introduced the infinitely divisible cascades in 1 dimension, a family of multifractal processes that can be easily synthesized numerically. This work extends the definition of infinitely divisible cascades from 1 dimension to d dimensions in the scalar case. Thus, a class of models is proposed both for data analysis and for numerical simulation in dimension d≥1. In this article, we give the definitions and main properties of infinitely divisible cascades in d dimensions. Then we focus on the modelling of statistical intermittency in turbulent flows. Several other applications are considered. [ABSTRACT FROM AUTHOR]

SECCHI-EUVI telescopes provide the first EUV images enabling a 3D reconstruction of solar coronal structures. We present a stereoscopic reconstruction method based on the Velociraptor algorithm, a multiscale optical-flow method that estimates displacement maps in sequences of EUV images. Following earlier calibration on sequences of SOHO-EIT data, we apply the algorithm to retrieve depth information from the two STEREO viewpoints using the SECCHI-EUVI telescope. We first establish a simple reconstruction formula that gives the radial distance to the centre of the Sun of a point identified both in EUVI-A and EUVI-B from the separation angle and the displacement map. We select pairs of images taken in the 30.4 nm passband of EUVI-A and EUVI-B, and apply a rigid transform from the EUVI-B image in order to set both images in the same frame of reference. The optical flow computation provides displacement maps from which we reconstruct a dense map of depths using the stereoscopic reconstruction formula. Finally, we discuss the estimation of the height of an erupting filament. [ABSTRACT FROM AUTHOR]

We study the statistical performance of multiresolution-based estimation procedures for the scaling exponents of multifractal processes. These estimators rely on the computation of multiresolution quantities such as wavelet, increment or aggregation coefficients. Estimates are obtained by linear fits performed in log of structure functions of order q versus log of scale plots. Using various and recent types of multiplicative cascades and a large variety of multifractal processes, we study and benchmark, by means of numerical simulations, the statistical performance of these estimation procedures. We show that they all undergo a systematic linearisation effect: for a range of orders q, the estimates account correctly for the scaling exponents; outside that range, the estimates significantly depart from the correct values and systematically behave as linear functions of q. The definition and characterisation of this effect are thoroughly studied. In contradiction with interpretations proposed in the literature, we provide numerical evidence leading to the conclusion that this linearisation effect is neither a finite size effect nor an infiniteness of moments effect, but that its origin should be related to the deep nature of the process itself. We comment on its importance and consequences for the practical analysis of the multifractal properties of empirical data. [ABSTRACT FROM AUTHOR]