Machine Learning and Bayesian Statistics for Seismic Compressive Sensing

Seismic surveys involve an artificial source of waves and a grid of receivers at the surface. Often, receivers could be missing either because they malfunctioned or could not be placed in certain locations. It could also be the fact that a local source of noise renders a receiver’s output as unusable. These gaps in the data cause problems in later stages of the seismic signal processing work flow via aliasing or incoherent noise and thus signal reconstruction is necessary. Modern algorithms utilise the principle of Compressive Sensing (CS) for reconstruction which uses the assumption that the signal of interest is either sparse in nature or in some other bases. Most algorithms are designed with the only aim to fill in gaps in the data without any consideration of learning bases or quantifying uncertainty in their predictions. In this thesis, we approach the seismic CS problem using probabilistic data-driven models that are adaptable to seismic data. We propose to use algorithms from the Bayesian statistics and machine learning field that allow the construction of models using probability distributions over random variables. This allows the modelling of sparsity and provides flexibility by adding or removing basis functions from the model. It also provides the framework for learning new dictionaries of bases, associating uncertainty for each prediction and denoising seismic signals. More specifically, we utilise two Bayesian algorithms for seismic CS, the Relevance Vector Machine (RVM) and the Beta Process Factor Analysis (BPFA). The RVM uses a sparsity promoting distribution over the coefficients of a linear combination of basis functions. By learning the appropriate parameters, the algorithm infers a predictive mean and predictive variance that is used for prediction of receivers’ values and uncertainty quantification. Experiments and comparisons on various seismic data show the effectiveness of the RVM with state-of-the-art reconstruction accuracy. Furthermore, its predictive variance is used along with modifications in order to create uncertainty maps with varying levels of correlation between uncertainty and respective reconstruction error of receivers. On the other hand, BPFA uses an alternative approach to enforce sparsity providing exact zero coefficients as opposed to the RVM. Another advantage is that it also learns the bases from the available data and provides denoising of seismic signals. Experiments and comparisons on seismic data show that the BPFA obtains state-of-the-art reconstruction accuracy on various domains. In addition, the learned bases are used by other algorithms to improve their performance. An analysis of the BPFA’s inference procedure is given along with insights to reduce its computational cost. We also utilise the probabilistic nature of the BPFA and calculate the variance of the receivers’ predictions obtained during inference. Using this, we create uncertainty maps that are highly correlated with the reconstruction error, obtaining better results than the RVM’s predictive variance. Finally, an analysis of seismic signals with different levels of variance is undertaken in order to provide guidance for the best choice of algorithm per region. The amount of seismic data available is growing, nevertheless quantity does not directly translate to quality. This creates the challenge to analyse and extract as much information and insight as possible. Using probabilistic data-driven models, we show how to achieve this by reconstructing seismic signals from under-sampled data, learn features from training data, denoise and create uncertainty maps for predictions in seismic surveys

Deep data compression for approximate ultrasonic image formation

In many ultrasonic imaging systems, data acquisition and image formation are performed on separate computing devices. Data transmission is becoming a bottleneck, thus, efficient data compression is essential. Compression rates can be improved by considering the fact that many image formation methods rely on approximations of wave-matter interactions, and only use the corresponding part of the data. Tailored data compression could exploit this, but extracting the useful part of the data efficiently is not always trivial. In this work, we tackle this problem using deep neural networks, optimized to preserve the image quality of a particular image formation method. The Delay-And-Sum (DAS) algorithm is examined which is used in reflectivity-based ultrasonic imaging. We propose a novel encoder-decoder architecture with vector quantization and formulate image formation as a network layer for end-to-end training. Experiments demonstrate that our proposed data compression tailored for a specific image formation method obtains significantly better results as opposed to compression agnostic to subsequent imaging. We maintain high image quality at much higher compression rates than the theoretical lossless compression rate derived from the rank of the linear imaging operator. This demonstrates the great potential of deep ultrasonic data compression tailored for a specific image formation method.Comment: IEEE International Ultrasonics Symposium 202

Deep learning for multi-view ultrasonic image fusion

Ultrasonic imaging is being used to obtain information about the acoustic properties of a medium by emitting waves into it and recording their interaction using ultrasonic transducer arrays. The Delay-And-Sum (DAS) algorithm forms images using the main path on which reflected signals travel back to the transducers. In some applications, different insonification paths can be considered, for instance by placing the transducers at different locations or if strong reflectors inside the medium are known a-priori. These different modes give rise to multiple DAS images reflecting different geometric information about the scatterers and the challenge is to either fuse them into one image or to directly extract higher-level information regarding the materials of the medium, e.g., a segmentation map. Traditional image fusion techniques typically use ad-hoc combinations of predefined image transforms, pooling operations and thresholding. In this work, we propose a deep neural network (DNN) architecture that directly maps all available data to a segmentation map while explicitly incorporating the DAS image formation for the different insonification paths as network layers. This enables information flow between data pre-processing and image post-processing DNNs, trained end-to-end. We compare our proposed method to a traditional image fusion technique using simulated data experiments, mimicking a non-destructive testing application with four image modes, i.e., two transducer locations and two internal reflection boundaries. Using our approach, it is possible to obtain much more accurate segmentation of defects

Single plane-wave imaging using physics-based deep learning

In plane-wave imaging, multiple unfocused ultrasound waves are transmitted into a medium of interest from different angles and an image is formed from the recorded reflections. The number of plane waves used leads to a tradeoff between frame-rate and image quality, with single-plane-wave (SPW) imaging being the fastest possible modality with the worst image quality. Recently, deep learning methods have been proposed to improve ultrasound imaging. One approach is to use image-to-image networks that work on the formed image and another is to directly learn a mapping from data to an image. Both approaches utilize purely data-driven models and require deep, expressive network architectures, combined with large numbers of training samples to obtain good results. Here, we propose a data-to-image architecture that incorporates a wave-physics-based image formation algorithm in-between deep convolutional neural networks. To achieve this, we implement the Fourier (FK) migration method as network layers and train the whole network end-to-end. We compare our proposed data-to-image network with an image-to-image network in simulated data experiments, mimicking a medical ultrasound application. Experiments show that it is possible to obtain high-quality SPW images, almost similar to an image formed using 75 plane waves over an angular range of ±16°. This illustrates the great potential of combining deep neural networks with physics-based image formation algorithms for SPW imaging

Fast ultrasonic imaging using end-to-end deep learning

Ultrasonic imaging algorithms used in many clinical and industrial applications consist of three steps: A data pre-processing, an image formation and an image post-processing step. For efficiency, image formation often relies on an approximation of the underlying wave physics. A prominent example is the Delay-And-Sum (DAS) algorithm used in reflectivity-based ultrasonic imaging. Recently, deep neural networks (DNNs) are being used for the data pre-processing and the image postprocessing steps separately. In this work, we propose a novel deep learning architecture that integrates all three steps to enable end-to-end trai

Deep Learning for Multi-View Ultrasonic Image Fusion

Ultrasonic imaging is being used to obtain information about the acoustic properties of a medium by emitting waves into it and recording their interaction using ultrasonic transducer arrays. The Delay-And-Sum (DAS) algorithm forms images using the main path on which reflected signals travel back to the transducers. In some applications, different insonification paths can be considered, for instance by placing the transducers at different locations or if strong reflectors inside the medium are known a-priori. These different modes give rise to multiple DAS images reflecting different geometric information about the scatterers and the challenge is to either fuse them into one image or to directly extract higher-level information regarding the materials of the medium, e.g., a segmentation map. Traditional image fusion techniques typically use ad-hoc combinations of pre-defined image transforms, pooling operations and thresholding. In this work, we propose a deep neural network (DNN) architecture that directly maps all available data to a segmentation map while explicitly incorporating the DAS image formation for the different insonification paths as network layers. This enables information flow between data pre-processing and image post-processing DNNs, trained end-to-end. We compare our proposed method to a traditional image fusion technique using simulated data experiments, mimicking a non-destructive testing application with four image modes, i.e., two transducer locations and two internal reflection boundaries. Using our approach, it is possible to obtain much more accurate segmentation of defects. Index Terms—deep learning, fast ultrasonic imaging, image fusion, boundary reflection

Deep Learning for Multi-View Ultrasonic Image Fusion

Ultrasonic imaging is being used to obtain information about the acoustic properties of a medium by emitting waves into it and recording their interaction using ultrasonic transducer arrays. The Delay-And-Sum (DAS) algorithm forms images using the main path on which reflected signals travel back to the transducers. In some applications, different insonification paths can be considered, for instance by placing the transducers at different locations or if strong reflectors inside the medium are known a-priori. These different modes give rise to multiple DAS images reflecting different geometric information about the scatterers and the challenge is to either fuse them into one image or to directly extract higher-level information regarding the materials of the medium, e.g., a segmentation map. Traditional image fusion techniques typically use ad-hoc combinations of pre-defined image transforms, pooling operations and thresholding. In this work, we propose a deep neural network (DNN) architecture that directly maps all available data to a segmentation map while explicitly incorporating the DAS image formation for the different insonification paths as network layers. This enables information flow between data pre-processing and image post-processing DNNs, trained end-to-end. We compare our proposed method to a traditional image fusion technique using simulated data experiments, mimicking a non-destructive testing application with four image modes, i.e., two transducer locations and two internal reflection boundaries. Using our approach, it is possible to obtain much more accurate segmentation of defects. Index Terms—deep learning, fast ultrasonic imaging, image fusion, boundary reflection

Fast ultrasonic imaging using end-to-end deep learning

Ultrasonic imaging algorithms used in many clinical and industrial applications consist of three steps: A data preprocessing, an image formation and an image post-processing step. For efficiency, image formation often relies on an approximation of the underlying wave physics. A prominent example is the Delay-And-Sum (DAS) algorithm used in reflectivity-based ultrasonic imaging. Recently, deep neural networks (DNNs) are being used for the data pre-processing and the image postprocessing steps separately. In this work, we propose a novel deep learning architecture that integrates all three steps to enable endto- end training. We examine turning the DAS image formation method into a network layer that connects data pre-processing layers with image post-processing layers that perform segmentation. We demonstrate that this integrated approach clearly outperforms sequential approaches that are trained separately. While network training and evaluation is performed only on simulated data, we also showcase the potential of our approach on real data from a non-destructive testing scenario. Index Terms—deep learning, end-to-end training, Delay-And- Sum, fast ultrasonic imaging, approximate inversion

Deep data compression for approximate ultrasonic image formation

In many ultrasonic imaging systems, data acquisition and image formation are performed on separate computing devices. Data transmission is becoming a bottleneck, thus, efficientdata compression is essential. Compression rates can be improved by considering the fact that many image formation methods rely on approximations of wave-matter interactions, and only use the corresponding part of the data. Tailored data compression could exploit this, but extracting the useful part of the data efficiently is not always trivial. In this work, we tackle this problem using deep neural networks, optimized to preserve the image quality of a particular image formation method. The Delay-And-Sum (DAS) algorithm is examined which is used in reflectivity-based ultrasonic imaging. We propose a novel encoder-decoder architecture with vector quantization and formulate image formation as a network layer for endto- end training. Experiments demonstrate that our proposed data compression tailored for a specific image formation method obtains significantly better results as opposed to compression agnostic to subsequent imaging. We maintain high image quality at much higher compression rates than the theoretical lossless compression rate derived from the rank of the linear imaging operator. This demonstrates the great potential of deep ultrasonic data compression tailored for a specific image formation method. Index Terms—deep learning, compression, Delay-And-Sum, fast ultrasonic imaging, end-to-end trainin

Deep data compression for approximate ultrasonic image formation

In many ultrasonic imaging systems, data acquisition and image formation are performed on separate computing devices. Data transmission is becoming a bottleneck, thus, efficientdata compression is essential. Compression rates can be improved by considering the fact that many image formation methods rely on approximations of wave-matter interactions, and only use the corresponding part of the data. Tailored data compression could exploit this, but extracting the useful part of the data efficiently is not always trivial. In this work, we tackle this problem using deep neural networks, optimized to preserve the image quality of a particular image formation method. The Delay-And-Sum (DAS) algorithm is examined which is used in reflectivity-based ultrasonic imaging. We propose a novel encoder-decoder architecture with vector quantization and formulate image formation as a network layer for endto- end training. Experiments demonstrate that our proposed data compression tailored for a specific image formation method obtains significantly better results as opposed to compression agnostic to subsequent imaging. We maintain high image quality at much higher compression rates than the theoretical lossless compression rate derived from the rank of the linear imaging operator. This demonstrates the great potential of deep ultrasonic data compression tailored for a specific image formation method. Index Terms—deep learning, compression, Delay-And-Sum, fast ultrasonic imaging, end-to-end trainin