Applied Numerical Analysis. By C.F. Gerald. Pp. xii, 340. £3·60. 1970. (Addison-Wesley.)

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The Essential Physics Of Medical Imaging

Conventional microwave imagers usually require either time-consuming data acquisition, or complicated reconstruction algorithms for data post-processing, making them largely ineffective for complex in-situ sensing and monitoring. Here, we experimentally report a real-time digital-metasurface imager that can be trained in-situ to generate the radiation patterns required by machine-learning optimized measurement modes. This imager is electronically reprogrammed in real time to access the optimized solution for an entire data set, realizing storage and transfer of full-resolution raw data in dynamically varying scenes. High-accuracy image coding and recognition are demonstrated in situ for various image sets, including hand-written digits and through-wall body gestures, using a single physical hardware imager, reprogrammed in real time. Our electronically controlled metasurface imager opens new venues for intelligent surveillance, fast data acquisition and processing, imaging at various frequencies, and beyond. Conventional imagers require time-consuming data acquisition, or complicated reconstruction algorithms for data post-processing. Here, the authors demonstrate a real-time digital-metasurface imager that can be trained in-situ to show high accuracy image coding and recognition for various image sets.

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Machine-learning reprogrammable metasurface imager.

Terahertz (THz) science and technology have greatly progressed over the past two decades to a point where the THz region of the electromagnetic spectrum is now a mature research area with many fundamental and practical applications. Furthermore, THz imaging is positioned to play a key role in many industrial applications, as THz technology is steadily shifting from university-grade instrumentation to commercial systems. In this context, the objective of this review is to discuss recent advances in THz imaging with an emphasis on the modalities that could enable real-time high-resolution imaging. To this end, we first discuss several key imaging modalities developed over the years: THz transmission, reflection, and conductivity imaging; THz pulsed imaging; THz computed tomography; and THz near-field imaging. Then, we discuss several enabling technologies for real-time THz imaging within the time-domain spectroscopy paradigm: fast optical delay lines, photoconductive antenna arrays, and electro-optic sampling with cameras. Next, we discuss the advances in THz cameras, particularly THz thermal cameras and THz field-effect transistor cameras. Finally, we overview the most recent techniques that enable fast THz imaging with single-pixel detectors: mechanical beam-steering, compressive sensing, spectral encoding, and fast Fourier optics. We believe that this critical and comprehensive review of enabling hardware, instrumentation, algorithms, and potential applications in real-time high-resolution THz imaging can serve a diverse community of fundamental and applied scientists.

Toward real-time terahertz imaging

Nonlinear electromagnetic (EM) inverse scattering is a quantitative and super-resolution imaging technique, in which more realistic interactions between the internal structure of scene and EM wavefield are taken into account in the imaging procedure, in contrast to conventional tomography. However, it poses important challenges arising from its intrinsic strong nonlinearity, ill-posedness, and expensive computational costs. To tackle these difficulties, we, for the first time to our best knowledge, exploit a connection between the deep neural network (DNN) architecture and the iterative method of nonlinear EM inverse scattering. This enables the development of a novel DNN-based methodology for nonlinear EM inverse problems (termed here DeepNIS). The proposed DeepNIS consists of a cascade of multilayer complex-valued residual convolutional neural network modules. We numerically and experimentally demonstrate that the DeepNIS outperforms remarkably conventional nonlinear inverse scattering methods in terms of both the image quality and computational time. We show that DeepNIS can learn a general model approximating the underlying EM inverse scattering system. It is expected that the DeepNIS will serve as powerful tool in treating highly nonlinear EM inverse scattering problems over different frequency bands, which are extremely hard and impractical to solve using conventional inverse scattering methods.

DeepNIS: Deep Neural Network for Nonlinear Electromagnetic Inverse Scattering

We introduce and analyze a new technique for model reduction for deep neural networks. While large networks are theoretically capable of learning arbitrarily complex models, overfitting and model redundancy negatively affects the prediction accuracy and model variance. Our Net-Trim algorithm prunes (sparsifies) a trained network layer-wise, removing connections at each layer by solving a convex optimization program. This program seeks a sparse set of weights at each layer that keeps the layer inputs and outputs consistent with the originally trained model. The algorithms and associated analysis are applicable to neural networks operating with the rectified linear unit (ReLU) as the nonlinear activation. We present both parallel and cascade versions of the algorithm. While the latter can achieve slightly simpler models with the same generalization performance, the former can be computed in a distributed manner. In both cases, Net-Trim significantly reduces the number of connections in the network, while also providing enough regularization to slightly reduce the generalization error. We also provide a mathematical analysis of the consistency between the initial network and the retrained model. To analyze the model sample complexity, we derive the general sufficient conditions for the recovery of a sparse transform matrix. For a single layer taking independent Gaussian random vectors of length $N$ as inputs, we show that if the network response can be described using a maximum number of $s$ non-zero weights per node, these weights can be learned from $\mathcal{O}(s\log N)$ samples.

Net-Trim: Convex Pruning of Deep Neural Networks with Performance Guarantee

In this paper, a parametric level set method for reconstruction of obstacles in general inverse problems is considered. General evolution equations for the reconstruction of unknown obstacles are derived in terms of the underlying level set parameters. We show that using the appropriate form of parameterizing the level set function results in a significantly lower dimensional problem, which bypasses many difficulties with traditional level set methods, such as regularization, reinitialization, and use of signed distance function. Moreover, we show that from a computational point of view, low order representation of the problem paves the way for easier use of Newton and quasi-Newton methods. Specifically for the purposes of this paper, we parameterize the level set function in terms of adaptive compactly supported radial basis functions, which, used in the proposed manner, provide flexibility in presenting a larger class of shapes with fewer terms. Also they provide a “narrow-banding” advantage which can further reduce the number of active unknowns at each step of the evolution. The performance of the proposed approach is examined in three examples of inverse problems, i.e., electrical resistance tomography, X-ray computed tomography, and diffuse optical tomography.

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Parametric Level Set Methods for Inverse Problems

In this paper, a parametric level set method for reconstruction of obstacles in general inverse problems is considered. General evolution equations for the reconstruction of unknown obstacles are derived in terms of the underlying level set parameters. We show that using the appropriate form of parameterizing the level set function results a significantly lower dimensional problem, which bypasses many difficulties with traditional level set methods, such as regularization, re-initialization and use of signed distance function. Moreover, we show that from a computational point of view, low order representation of the problem paves the path for easier use of Newton and quasi-Newton methods. Specifically for the purposes of this paper, we parameterize the level set function in terms of adaptive compactly supported radial basis functions, which used in the proposed manner provides flexibility in presenting a larger class of shapes with fewer terms. Also they provide a "narrow-banding" advantage which can further reduce the number of active unknowns at each step of the evolution. The performance of the proposed approach is examined in three examples of inverse problems, i.e., electrical resistance tomography, X-ray computed tomography and diffuse optical tomography.

Spatial resolution, spectral contrast and occlusion are three major bottlenecks for non-invasive inspection of complex samples with current imaging technologies. We exploit the sub-picosecond time resolution along with spectral resolution provided by terahertz time-domain spectroscopy to computationally extract occluding content from layers whose thicknesses are wavelength comparable. The method uses the statistics of the reflected terahertz electric field at subwavelength gaps to lock into each layer position and then uses a time-gated spectral kurtosis to tune to highest spectral contrast of the content on that specific layer. To demonstrate, occluding textual content was successfully extracted from a packed stack of paper pages down to nine pages without human supervision. The method provides over an order of magnitude enhancement in the signal contrast and can impact inspection of structural defects in wooden objects, plastic components, composites, drugs and especially cultural artefacts with subwavelength or wavelength comparable layers.

Terahertz time-gated spectral imaging for content extraction through layered structures

This paper presents a new joint inversion approach to shape-based inverse problems. Given two sets of data from distinct physical models, the main objective is to obtain a unified characterization of inclusions within the spatial domain of the physical properties to be reconstructed. Although our proposed method generally applies to many types of inversion problems, the main motivation here is to characterize subsurface contaminant source-zones by processing down gradient hydrological data and cross-gradient electrical resistance tomography (ERT) observations. Inspired by Newton's method for multi-objective optimization, we present an iterative inversion scheme that suggests taking descent steps that can simultaneously reduce both data-model misfit terms. Such an approach, however, requires solving a non-smooth convex problem at every iteration, which is computationally expensive for a pixel-based inversion over the whole domain. Instead, we employ a parametric level set (PaLS) technique that substantially reduces the number of underlying parameters, making the inversion computationally tractable. The performance of the technique is examined and discussed through the reconstruction of source zone architectures that are representative of dense non-aqueous phase liquid (DNAPL) contaminant release in a statistically homogenous sandy aquifer. In these examples, the geometric configuration of the DNAPL mass is considered along with additional information about its spatial variability within the contaminated zone, such as the identification of low and high saturation regions. Comparison of the reconstructions with the true DNAPL architectures highlights the superior performance of the model-based technique and joint inversion scheme.

Alireza Aghasi

Papers

Net-Trim: Convex Pruning of Deep Neural Networks with Performance Guarantee

Parametric Level Set Methods for Inverse Problems

Parametric Level Set Methods for Inverse Problems

Terahertz time-gated spectral imaging for content extraction through layered structures

A Geometric Approach to Joint Inversion with Applications to Contaminant Source Zone Characterization