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Abstract In this paper we consider the problem of recovering a low-rank Tucker approximation to a massive tensor based solely on structured random compressive measurements (i.e., a sketch). Crucially, the proposed random measurement ensembles are both designed to be compactly represented (i.e., low-memory), and can also be efficiently computed in one-pass over the tensor. Thus, the proposed compressive sensing approach may be used to produce a low-rank factorization of a huge tensor that is too large to store in memory with a total memory footprint on the order of the much smaller desired low-rank factorization. In addition, the compressive sensing recovery algorithm itself (which takes the compressive measurements as input, and then outputs a low-rank factorization) also runs in a time which principally depends only on the size of the sought factorization, making its runtime sub-linear in the size of the large tensor one is approximating. Finally, unlike prior works related to (streaming) algorithms for low-rank tensor approximation from such compressive measurements, we present a unified analysis of both Kronecker and Khatri-Rao structured measurement ensembles culminating in error guarantees comparing the error of our recovery algorithm’s approximation of the input tensor to the best possible low-rank Tucker approximation error achievable for the tensor by any possible algorithm. We further include an empirical study of the proposed approach that verifies our theoretical findings and explores various trade-offs of parameters of interest. 

The Citizen CATE 2024 next-generation experiment placed 43 identical telescope and camera setups along the path of totality during the total solar eclipse (TSE) on 8 April 2024 to capture a 60-minute movie of the inner and middle solar corona in polarized visible light. The 2024 TSE path covered a large geographic swath of North America and we recruited and trained 36 teams of community participants (“citizen scientists”) representative of the various communities along the path of totality. Afterwards, these teams retained the equipment in their communities for on-going education and public engagement activities. Participants ranged from students (K12, undergraduate, and graduate), educators, and adult learners to amateur and professional astronomers. In addition to equipment for their communities, CATE 2024 teams received hands-on telescope training, educational and learning materials, and instruction on data analysis techniques. CATE 2024 used high-cadence, high-dynamic-range (HDR) polarimetric observations of the solar corona to characterize the physical processes that shape its heating, structure, and evolution at scales and sensitivities that cannot be studied outside of a TSE. Conventional eclipse observations do not span sufficient time to capture changing coronal topology, but the extended observation from CATE 2024 does. Analysis of the fully calibrated dataset will provide deeper insight and understanding into these critical physical processes. We present an overview of the CATE 2024 project, including how we engaged local communities along the path of totality, and the first look at CATE 2024 data products from the 2024 TSE.