Using wavelet decomposition to determine the dimension of structures from projected images.
basic_science · Level V
Where this comes from
- Record sourced from PubMed, PMID 41871239.
- Also identified by DOI 10.1073/pnas.2534122123 and PMC identifier 13037944.
- Licence recorded as CC BY.
- The licence permits redistribution, so the abstract is shown in full and the full text is available from the publisher.
Abstract
Mesoscale structures in turbulent media can often be described as fractional dimensional across a wide range of scales. The goal of this paper is to determine the structure's dimension from a projected image. Our method exploits the laws of scaling of wavelet power spectra under projection and does not carry any restrictions on the embedding and projected dimensions. We show that the wavelet power spectrum of a projected <i>γ</i> dimensional measure is [Formula: see text], where <i>j</i> is the wavelet scale. We contrast the wavelet method with the popular box-counting approach. For projected images, the use of box-counting at fixed thresholds often leads to erroneous results. We apply the method to James Webb Space Telescope (JWST) infrared and Chandra X-ray observations of the supernova remnant Cassiopeia A. We find that the emissions can be represented by projections of mesoscale substructures with fractal dimensions varying from [Formula: see text] for the warm CO layer observed by JWST, up to [Formula: see text] for the hot X-ray emitting gas layer in the supernova remnant.