A new X-ray computed tomography technique for the purpose of imaging fluidized beds is presented. It consists of an experimental set-up with three stationary X-ray source and flat panel detector pairs, a geometric calibration and data processing workflow, and an image reconstruction algorithm. The technique enables sparse-angular tomographic reconstruction in large 3D regions of fluidized beds at framerates up to 200 Hz, and therefore images bubbles along their whole trajectories through the volume. It allows for a unique analysis of bubble dynamics in fluidized beds, including bubble velocities, bubble transformations, i.e., time evolution of the bubble distributions in space, and bubble–bubble interactions. In this article, we first analyze the main limitation of the technique, the sparse angular resolution, through numerical simulations. We then test the experimental set-up through imaging a series of phantoms. Lastly, we demonstrate results from a Geldart B bubbling fluidized bed.

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Optical measurements often exhibit mixed Poisson–Gaussian noise statistics, which hampers the image quality, particularly under low signal-to-noise ratio (SNR) conditions. Computational imaging falls short in such situations when solely Poissonian noise statistics are assumed. In response to this challenge, we define a loss function that explicitly incorporates this mixed noise nature. By using a maximum-likelihood estimation, we devise a practical method to account for a camera readout noise in gradient-based ptychography optimization. Our results, based on both experimental and numerical data, demonstrate that this approach outperforms the conventional one, enabling enhanced image reconstruction quality under challenging noise conditions through a straightforward methodological adjustment.

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Our understanding of the past behavior of the geomagnetic field arises from magnetic signals stored in geological materials, e.g., (volcanic) rocks. Bulk rock samples, however, often contain magnetic grains that differ in chemistry, size, and shape; some of them record the Earth's magnetic field well, others are unreliable. The presence of a small amount of adverse behaved magnetic grains in a sample may already obscure important information on the past state of the geomagnetic field. Recently it was shown that it is possible to determine magnetizations of individual grains in a sample by combining X-ray computed tomography and magnetic surface scanning measurements. Here we establish this new Micromagnetic Tomography (MMT) technique and make it suitable for use with different magnetic scanning techniques, and for both synthetic and natural samples. We acquired reliable magnetic directions by selecting subsets of grains in a synthetic sample, and we obtained rock-magnetic information of individual grains in a volcanic sample. This illustrates that MMT opens up entirely new venues of paleomagnetic and rock-magnetic research. MMT's unique ability to determine the magnetization of individual grains in a nondestructive way allows for a systematic analysis of how geological materials record and retain information on the past state of the Earth's magnetic field. Moreover, by interpreting only the contributions of known magnetically well-behaved grains in a sample, MMT has the potential to unlock paleomagnetic information from even the most complex, crucial, or valuable recorders that current methods are unable to recover.

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Our understanding of the behavior of the geomagnetic field arises from magnetic signals stored in geological materials, e.g. lavas. Almost all experiments to determine the past state of the Earth’s magnetic field use bulk samples (typically 1 - 10 cc) and measure their magnetic moment after series of laboratory treatments. Lavas, however, consist of mixtures of different iron-oxide grains that vary in size, shape, and chemistry. Some of these grains are good recorders of the Earth’s magnetic field; others are not. Only a small amount of adverse behaved magnetic grains in a sample already hampers all classical experiments to obtain paleointensities; success rates as low as 10-20% are common, i.e. for 80-90% of all lavas vital information on paleointensities is lost before it can be uncovered. Recently, we showed that it is possible to determine the magnetization of individual grains inside a synthetic sample using a new technique: Micromagnetic Tomography. The individual magnetizations of grains are determined by inverting scanning magnetometry data from the surface on the sample onto the known locations, sizes and shapes of the magnetic grains that are obtained from a microCT scan of the sample. The synthetic sample used for our proof-of-concept, however, was optimized for success: the dispersion of magnetic markers was low, and the magnetite grains had a well-defined grain size range. Furthermore, the scanning SQUID microscope used requires the sample to be at 4 K, below the Verweij transition of the magnetite grains. Here we present the first Micromagnetic Tomography results from natural samples. We used two magnetic scanning techniques that operate at room temperature, a Magnetic Tunneling Junction set-up and a Quantum Diamond Magnetometer, to acquire the magnetic surface scans from a Hawaiian lava and calculated magnetic moments of individual grains present. We show that it is possible to acquire rock magnetic information as function of grain size from these natural samples and reveal the first results of interpreting a paleomagnetic direction from selected subsets of grains in our samples. These are the first steps towards deriving rock magnetic and paleomagnetic information from subsets of known good recorders inside lava samples, a technique that will revolutionize our field of research.@en

As a result of the shallow depth of focus of the optical imaging system, the use of standard filtered back projection in optical projection tomography causes space-variant tangential blurring that increases with the distance to the rotation axis. We present a novel optical tomographic image reconstruction technique that incorporates the point spread function of the imaging lens in an iterative reconstruction. The technique is demonstrated using numerical simulations, tested on experimental optical projection tomography data of single fluorescent beads, and applied to high-resolution emission optical projection tomography imaging of an entire zebrafish larva. Compared to filtered back projection our results show greatly reduced radial and tangential blurring over the entire 5.2x5.2 mm2 field of view, and a significantly improved signal to noise ratio.@en

Seismic full-waveform inversion tries to estimate subsurface medium parameters from seismic data. Areas with subsurface salt bodies are of particular interest because they often have hydrocarbon reservoirs on their sides or underneath. Accurate reconstruction of their geometry is a challenge for current techniques. This paper presents a parametric level-set method for the reconstruction of salt-bodies in seismic full-waveform inversion. We split the subsurface model in two parts: a background velocity model and a salt body with known velocity but undetermined shape. The salt geometry is represented by a level-set function that evolves during the inversion. We choose radial basis functions to represent the level-set function, leading to an optimization problem with a modest number of parameters. A common problem with level-set methods is to fine-tune the width of the level-set boundary for optimal sensitivity. We propose a robust algorithm that dynamically adapts the width of the level-set boundary to ensure faster convergence. Tests on a suite of idealized salt geometries show that the proposed method is stable against a modest amount of noise. We also extend the method to joint inversion of both the background velocity model and the salt geometry.@en

Full-waveform inversion attempts to estimate a high-resolution model of the Earth by inverting all the seismic data. This procedure fails if the Earth model contains high-contrast bodies such as salt and if su ciently low frequencies are absent from the data. Salt bodies are important for hydrocarbon exploration because oil or gas reservoirs are often located on their sides or underneath. We represent the shape of the salt body with a level set, constructed from radial basis functions to keep its dimensionality low. We have shown earlier that the salt body can be completely recovered if the sediment structure is already known. In this paper, we propose a strategy to simultaneously reconstruct the sediment and the salt. The sediment is implicitly represented by a bilinear interpolation kernel with a small number of variables. An alternating minimization technique solves the resulting optimization problem. The results on a synthetic model using Gauss-Newton approximation of the Hessian shows the feasibility of the approach@en

Seismic full-waveform inversion has become a popular technique for imaging the subsurface from seismic data. The reconstruction of the subsurface medium parameters becomes challenging in the presence of sharp contrasts such as salt bodies. We address the problem by splitting the subsurface model in two parts: a background velocity model and a salt body with known constant velocity but undetermined shape. The salt geometry is represented by a level-set function parametrized by radial basis functions. This leads to a non-linear optimization problem with a modest number of parameters. We improve the convergence speed by utilizing second-order updates from Gauss-Newton Hessian. Tests on the suite of idealized salt models show that the proposed method accurately determines the salt geometry in the presence of a modest amount of noise.@en

In seismic exploration, the delineation of large bodies with hard exterior contrasts but nearly constant interior properties is a challenge. Examples include salt diapirs, salt slabs, anhydrite or basalt layers. Salt geometries are of particular interest because they often have hydrocarbon reservoirs on their sides or underneath. This papers introduces a parametric level-set method for the reconstruction of such geometries in seismic full-waveform inversion (FWI). The level-set determines the outline of the salt geometry and evolves during the inversion in terms of its underlying parameters. For the latter, we employ Gaussian radial basis functions that can represent a large class of shapes with a small number of parameters. This keeps the dimensionality of the inverse problem small, which makes it easier to solve. First tests on a simple 2-D square box model show dramatic improvements over classic FWI.@en