Most reconstruction algorithms for photoacoustic imaging assume that the pressure field is measured by ultrasound sensors placed on a detection surface. However, such sensors do not measure pressure exactly due to their non-uniform directional and frequency responses, and resolution limitations. This is the case for piezoelectric sensors that are commonly employed for photoacoustic imaging. In this paper, using the method of matched asymptotic expansions and the basic constitutive relations for piezoelectricity, we propose a simple mathematical model for piezoelectric transducers. The approach simultaneously models how the pressure waves induce the piezoelectric measurements and how the presence of the sensors affects the pressure waves. Using this model, we analyze whether the data
gathered by piezoelectric sensors leads to the mathematical solvability of the photoacoustic imaging problem. We conclude that this imaging problem is well-posed in certain normed spaces and under a geometric assumption. We also propose an iterative reconstruction algorithm that incorporates the model for piezoelectric measurements. A numerical implementation of the reconstruction algorithm is presented.
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Sparse signal recovery from modulo observations
Abstract We consider the problem of reconstructing a signal from under-determined modulo observations (or measurements). This observation model is inspired by a relatively new imaging mechanism called modulo imaging, which can be used to extend the dynamic range of imaging systems; variations of this model have also been studied under the category of phase unwrapping. Signal reconstruction in the under-determined regime with modulo observations is a challenging ill-posed problem, and existing reconstruction methods cannot be used directly. In this paper, we propose a novel approach to solving the signal recovery problem under sparsity constraints for the special case to modulo folding limited to two periods. We show that given a sufficient number of measurements, our algorithm perfectly recovers the underlying signal. We also provide experiments validating our approach on toy signal and image data and demonstrate its promising performance.
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- NSF-PAR ID:
- 10311124
- Date Published:
- Journal Name:
- EURASIP Journal on Advances in Signal Processing
- Volume:
- 2021
- Issue:
- 1
- ISSN:
- 1687-6180
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Abstract Purpose Parallel imaging and compressed sensing reconstructions of large MRI datasets often have a prohibitive computational cost that bottlenecks clinical deployment, especially for three‐dimensional (3D) non‐Cartesian acquisitions. One common approach is to reduce the number of coil channels actively used during reconstruction as in coil compression. While effective for Cartesian imaging, coil compression inherently loses signal energy, producing shading artifacts that compromise image quality for 3D non‐Cartesian imaging. We propose coil sketching, a general and versatile method for computationally‐efficient iterative MR image reconstruction.
Theory and Methods We based our method on randomized sketching algorithms, a type of large‐scale optimization algorithms well established in the fields of machine learning and big data analysis. We adapt the sketching theory to the MRI reconstruction problem via a structured sketching matrix that, similar to coil compression, considers high‐energy virtual coils obtained from principal component analysis. But, unlike coil compression, it also considers random linear combinations of the remaining low‐energy coils, effectively leveraging information from all coils.
Results First, we performed ablation experiments to validate the sketching matrix design on both Cartesian and non‐Cartesian datasets. The resulting design yielded both improved computatioanal efficiency and preserved signal‐to‐noise ratio (SNR) as measured by the inverse g‐factor. Then, we verified the efficacy of our approach on high‐dimensional non‐Cartesian 3D cones datasets, where coil sketching yielded up to three‐fold faster reconstructions with equivalent image quality.
Conclusion Coil sketching is a general and versatile reconstruction framework for computationally fast and memory‐efficient reconstruction.
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Optical metasurfaces consist of densely arranged unit cells that manipulate light through various light confinement and scattering processes. Due to its unique advantages, such as high performance, small form factor and easy integration with semiconductor devices, metasurfaces have been gathering increasing attention in fields such as displays, imaging, sensing and optical computation. Despite advances in fabrication and characterization, a viable design prediction for suitable optical response remains challenging for complex optical metamaterial systems. The computation cost required to obtain the optimal design exponentially grows as the design complexity increases. Furthermore, the design prediction is challenging since the inverse problem is often ill-posed. In recent years, deep learning (DL) methods have shown great promise in the area of inverse design. Inspired by this and the capability of DL to produce fast inference, we introduce a physics-informed DL framework to expedite the computation for the inverse design of metasurfaces. Addition of the physics-based constraints improve generalizability of the DL model while reducing data burden. Our approach introduces a tandem DL architecture with physics-based learning to alleviate the nonuniqueness issue by selecting designs that are scientifically consistent, with low error in design prediction and accurate reconstruction of optical responses. To prove the concept, we focus on the inverse design of a representative plasmonic device that consists of metal gratings deposited on a dielectric film on top of a metal substrate. The optical response of the device is determined by the geometrical dimensions as well as the material properties. The training and testing data are obtained through Rigorous Coupled-Wave Analysis (RCWA), while the physics-based constraint is derived from solving the electromagnetic (EM) wave equations for a simplified homogenized model. We consider the prediction of design for the optical response of a single wavelength incident or a spectrum of wavelength in the visible light range. Our model converges with an accuracy up to 97% for inverse design prediction with the optical response for the visible light spectrum as input. The model is also able to predict design with accuracy up to 96% and optical response reconstruction accuracy of 99% for optical response of a single wavelength of light as input.more » « less
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Computational image reconstruction algorithms generally produce a single image without any measure of uncertainty or confidence. Regularized Maximum Likelihood (RML) and feed-forward deep learning approaches for inverse problems typically focus on recovering a point estimate. This is a serious limitation when working with under-determined imaging systems, where it is conceivable that multiple image modes would be consistent with the measured data. Characterizing the space of probable images that explain the observational data is therefore crucial. In this paper, we propose a variational deep probabilistic imaging approach to quantify reconstruction uncertainty. Deep Probabilistic Imaging (DPI) employs an untrained deep generative model to estimate a posterior distribution of an unobserved image. This approach does not require any training data; instead, it optimizes the weights of a neural network to generate image samples that fit a particular measurement dataset. Once the network weights have been learned, the posterior distribution can be efficiently sampled. We demonstrate this approach in the context of interferometric radio imaging, which is used for black hole imaging with the Event Horizon Telescope, and compressed sensing Magnetic Resonance Imaging (MRI).more » « less
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SUMMARY The ability to accurately and reliably obtain images of shallow subsurface anomalies within the Earth is important for hazard monitoring and a fundamental understanding of many geologic structures, such as volcanic edifices. In recent years, machine learning (ML) has gained increasing attention as a novel approach for addressing complex problems in the geosciences. Here we present an ML-based inversion method to integrate cosmic-ray muon and gravity data sets for shallow subsurface density imaging at a volcano. Starting with an ensemble of random density anomalies, we use physics-based forward calculations to find the corresponding set of expected gravity and muon attenuation observations. Given a large enough ensemble of synthetic density patterns and observations, the ML algorithm is trained to recognize the expected spatial relations within the synthetic input–output pairs, learning the inherent physical relationships between them. Once trained, the ML algorithm can then interpolate the best-fitting anomalous pattern given data that were not used in training, such as those obtained from field measurements. We test the validity of our ML algorithm using field data from the Showa-Shinzan lava dome (Mt Usu, Japan) and show that our model produces results consistent with those obtained using a more traditional Bayesian joint inversion. Our results are similar to the previously published inversion, and suggest that the Showa-Shinzan lava dome consists of a relatively high-density (2200–2400 km m–3) cylindrical anomaly, about 300 m in diameter. Adding noise to synthetic training and testing data sets shows that, as expected, the ML algorithm is most robust in areas of high sensitivity, as determined by the forward kernels. Overall, we discover that ML offers a viable alternate method to a Bayesian joint inversion when used with gravity and muon data sets for subsurface density imaging.
- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1186/s13634-021-00722-w
