Optimal restoration of noisy 3D X-ray data via shearlet

decomposition

Regularization with optimal space-time priors

We propose a variational regularization approach based on cylindrical shearlets to deal with dynamic imaging problems, with dynamic tomography as guiding example. The idea is that the mismatch term essentially integrates a sequence of separable, static problems, while the regularization term sees the non-stationary target as a spatio-temporal object. We motivate this approach by showing that cylindrical shearlets provide optimally sparse approximations for the class of cartoon-like videos, i.e., a class of functions useful to model spatio-temporal image sequences and videos, which we introduce extending the classic notion of cartoon-like images. To formulate our regularization model, we define cylindrical shearlet smoothness spaces, which is pivotal to obtain suitable embeddings in functional spaces. To complete our analysis, we prove that the proposed regularization strategy is well-defined, the solution of the minimisation problem exists and is unique (for $p > 1$). Furthermore, we provide convergence rates (in terms of the symmetric Bregman distance) under deterministic and random noise conditions, and within the context of statistical inverse learning. We numerically validate our theoretical results using both simulated and measured dynamic tomography data, showing that our approach leads to a practical and robust reconstruction strategy.Comment: 51 pages, 11 figure

A Method to Improve the Flood Maps Forecasted by On-Line Use of 1D Model

Forecasting floods in urban areas during a heavy rainfall is the aim of every early warning system. 2D-models produce the most accurate flood maps, but they are practically useless as quasi real-time tools, because their run times are comparable to times of propagation of floods. Run times of 1D-model are of tens of seconds, but their predictions lack accuracy and many useful indicators of flood severity. Our aim is the identification of the 2D-model map that is more similar to the actual map, chosen among those simulated off-line. To this aim, we produce a rough flood map of the occurring event, through a quasi real-time simulation of the rainfall-runoff using a 1D-model. Then we apply an original method, named "ranking approach", to perform the best matching. This method is applied to the Corace torrent (Calabria, Southern Italy), using 17 synthetic hyetographs to simulate the same number of rainfall-runoff events, using 1D (SWMM) and 2D (MIKE) models. The method proves to be effective in 65% of the cases, while in 82% of cases (i.e., for 14 cases out 17), the event produced by the same ietograph falls within the third rank

Super-resolved compressive demonstrator for Earth Observation applications in the Medium Infrared: instrumental concept, optical design and expected performances

Earth Observation (EO) systems are generating an ever-increasing amount of data to be handled on board yet with limited resources, which sometimes hinders a full exploitation of the information content. In this paper, we present a demonstrator of a super-resolved compressive imager operating in whiskbroom mode in the Visible-Near Infrared (VISNIR) and Medium Infrared (MIR) spectral ranges. The demonstrator, which is under development in the frame of the EU H2020 funded SURPRISE project, is based on the use of a Digital MicroMirror Device (DMD) as a core element of its architecture and it is inspired by a single-pixel camera in order to avoid the use of large focal plane arrays. The demonstrator has 10 channels in the VNIR and two channels in the MIR and it can reach a super-resolution factor from 4 x 4 to 32 x 32, that is the ratio between the number of pixels of the image reconstructed at the end of the process and the number of pixels of the detector. Besides, on the grounds of the results obtained by image reconstruction tests on simulated datasets by using Deep Learning based algorithms, data are expected to be natively compressed with a Compression Ratio up to 50%. The study is expected to provide valuable insight for the future development of a novel class of EO instruments with improved performances in terms of ground sampling distance, native compression and on-board processing capabilities. Additional presentation content can be accessed on the supplemental content page

The SURPRISE demonstrator: a super-resolved compressive instrument in the visible and medium infrared for Earth Observation

While Earth Observation (EO) data has become ever more vital to understanding the planet and addressing societal challenges, applications are still limited by revisit time and spatial resolution. Though low Earth orbit missions can achieve resolutions better than 100 m, their revisit time typically stands at several days, limiting capacity to monitor dynamic events. Geostationary (GEO) missions instead typically provide data on an hour-basis but with spatial resolution limited to 1 km, which is insufficient to understand local phenomena. In this paper, we present the SURPRISE project - recently funded in the frame of the H2020 programme – that gathers the expertise from eight partners across Europe to implement a demonstrator of a super-spectral EO payload - working in the visible (VIS) - Near Infrared (NIR) and in the Medium InfraRed (MIR) and conceived to operate from GEO platform -with enhanced performance in terms of at-ground spatial resolution, and featuring innovative on-board data processing and encryption functionalities. This goal will be achieved by using Compressive Sensing (CS) technology implemented via Spatial Light Modulators (SLM). SLM-based CS technology will be used to devise a super-resolution configuration that will be exploited to increase the at-ground spatial resolution of the payload, without increasing the number of detector’s sensing elements at the image plane. The CS approach will offer further advantages for handling large amounts of data, as is the case of superspectral payloads with wide spectral and spatial coverage. It will enable fast on-board processing of acquired data for information extraction, as well as native data encryption on top of native compression. SURPRISE develops two disruptive technologies: Compressive Sensing (CS) and Spatial Light Modulator (SLM). CS optimises data acquisition (e.g. reduced storage and transmission bandwidth requirements) and enables novel onboard processing and encryption functionalities. SLM here implements the CS paradigm and achieves a super-resolution architecture. SLM technology, at the core of the CS architecture, is addressed by: reworking and testing off-the-shelf parts in relevant environment; developing roadmap for a European SLM, micromirror array-type, with electronics suitable for space qualification. By introducing for the first time the concept of a payload with medium spatial resolution (few hundreds of meters) and near continuous revisit (hourly), SURPRISE can lead to a EO major breakthrough and complement existing operational services. CS will address the challenge of large data collection, whilst onboard processing will improve timeliness, shortening time needed to extract information from images and possibly generate alarms. Impact is relevant to industrial competitiveness, with potential for market penetration of the demonstrator and its components

Spatial Light Modulator-Based Architecture to Implement a Super-Resolved Compressive Instrument for Earth Observation

Due to a growing interest for imagery with high spatial and spectral resolution, Earth Observation sensors are producing increasing amounts of data. This poses a severe challenge in terms of computational, memory and transmission requirements. In order to overcome these limitations, a fascinating approach is the implementation of a compressive sensing architecture. In this paper, we present an instrumental concept based on the use of a spatial light modulator to implement a super-resolved, compressive demonstrator of an instrument aimed at Earth Observation in the visible and medium infrared spectral regions from geostationary platform

Optimally sparse shearlet approximations of 3D data

Sparse representations of multidimensional data have gained more and more prominence in recent years, in response to the need to process large and multi-dimensional data sets arising from a variety of applications in a timely and effective manner. This is especially important in applications such as remote sensing, satellite imagery, scientific simulations and electronic surveillance. Directional multiscale systems such as shearlets are able to provide sparse representations thanks to their ability to approximate anisotropic features much more efficiently than traditional multiscale representations. In this paper, we show that the shearlet approach is essentially optimal in representing a large class of 3D containing discontinuities along surfaces. This is the first nonadaptive approach to achieve provably optimal sparsity properties in the 3D setting

A directional representation for 3D tubular structures resulting from isotropic well-localized

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