Optimization of Array Encoding for Ultrasound Imaging

Objective: The transmit encoding model for synthetic aperture imaging is a robust and flexible framework for understanding the effect of acoustic transmission on ultrasound image reconstruction. Our objective is to use machine learning (ML) to construct scanning sequences, parameterized by time delays and apodization weights, that produce high quality B-mode images. Approach: We use an ML model in PyTorch and simulated RF data from Field II to probe the space of possible encoding sequences for those that minimize a loss function that describes image quality. This approach is made computationally feasible by a novel formulation of the derivative for delay-and-sum beamforming. We demonstrate these results experimentally on wire targets and a tissue-mimicking phantom. Main Results: When trained according to a given set of imaging parameters (imaging domain, hardware restrictions), our ML imaging model produces optimized encoding sequences that improve a number of standard quality metrics including resolution, field of view, and contrast, over conventional sequences. Significance: This work demonstrates that the set of encoding schemes that are commonly used represent only a narrow subset of those available. Additionally, it demonstrates the value for ML tasks in synthetic transmit aperture imaging to consider the beamformer within the model, instead of as purely post-processing.

Variational Entropy Search for Adjusting Expected Improvement

Bayesian optimization is a widely used technique for optimizing black-box functions, with Expected Improvement (EI) being the most commonly utilized acquisition function in this domain. While EI is often viewed as distinct from other information-theoretic acquisition functions, such as entropy search (ES) and max-value entropy search (MES), our work reveals that EI can be considered a special case of MES when approached through variational inference (VI). In this context, we have developed the Variational Entropy Search (VES) methodology and the VES-Gamma algorithm, which adapts EI by incorporating principles from information-theoretic concepts. The efficacy of VES-Gamma is demonstrated across a variety of test functions and read datasets, highlighting its theoretical and practical utilities in Bayesian optimization scenarios.

In Situ Framework for Coupling Simulation and Machine Learning with Application to CFD

Recent years have seen many successful applications of machine learning (ML) to facilitate fluid dynamic computations. As simulations grow, generating new training datasets for traditional offline learning creates I/O and storage bottlenecks. Additionally, performing inference at runtime requires non-trivial coupling of ML framework libraries with simulation codes. This work offers a solution to both limitations by simplifying this coupling and enabling in situ training and inference workflows on heterogeneous clusters. Leveraging SmartSim, the presented framework deploys a database to store data and ML models in memory, thus circumventing the file system. On the Polaris supercomputer, we demonstrate perfect scaling efficiency to the full machine size of the data transfer and inference costs thanks to a novel co-located deployment of the database. Moreover, we train an autoencoder in situ from a turbulent flow simulation, showing that the framework overhead is negligible relative to a solver time step and training epoch.

Bi-fidelity Variational Auto-encoder for Uncertainty Quantification

Quantifying the uncertainty of quantities of interest (QoIs) from physical systems is a primary objective in model validation. However, achieving this goal entails balancing the need for computational efficiency with the requirement for numerical accuracy. To address this trade-off, we propose a novel bi-fidelity formulation of variational auto-encoders (BF-VAE) designed to estimate the uncertainty associated with a QoI from low-fidelity (LF) and high-fidelity (HF) samples of the QoI. This model allows for the approximation of the statistics of the HF QoI by leveraging information derived from its LF counterpart. Specifically, we design a bi-fidelity auto-regressive model in the latent space that is integrated within the VAE's probabilistic encoder-decoder structure. An effective algorithm is proposed to maximize the variational lower bound of the HF log-likelihood in the presence of limited HF data, resulting in the synthesis of HF realizations with a reduced computational cost. Additionally, we introduce the concept of the bi-fidelity information bottleneck (BF-IB) to provide an information-theoretic interpretation of the proposed BF-VAE model. Our numerical results demonstrate that BF-VAE leads to considerably improved accuracy, as compared to a VAE trained using only HF data when limited HF data is available.

The Dependence of Parallel Imaging with Linear Predictability on the Undersampling Direction

Parallel imaging with linear predictability takes advantage of information present in multiple receive coils to accurately reconstruct the image with fewer samples. Commonly used algorithms based on linear predictability include GRAPPA and SPIRiT. We present a sufficient condition for reconstruction based on the direction of undersampling and the arrangement of the sensing coils. This condition is justified theoretically and examples are shown using real data. We also propose a metric based on the fully-sampled auto-calibration region which can show which direction(s) of undersampling will allow for a good quality image reconstruction.

QCNN: Quadrature Convolutional Neural Network with Application to Unstructured Data Compression

We present a new convolution layer for deep learning architectures which we call QuadConv -- an approximation to continuous convolution via quadrature. Our operator is developed explicitly for use on unstructured data, and accomplishes this by learning a continuous kernel that can be sampled at arbitrary locations. In the setting of neural compression, we show that a QuadConv-based autoencoder, resulting in a Quadrature Convolutional Neural Network (QCNN), can match the performance of standard discrete convolutions on structured uniform data, as in CNNs, and maintain this accuracy on unstructured data.

Superresolution photoacoustic tomography using random speckle illumination and second order moments

Idier et al. [IEEE Trans. Comput. Imaging 4(1), 2018] propose a method which achieves superresolution in the microscopy setting by leveraging random speckle illumination and knowledge about statistical second order moments for the illumination patterns and model noise. This is achieved without any assumptions on the sparsity of the imaged object. In this paper, we show that their technique can be extended to photoacoustic tomography. We propose a simple algorithm for doing the reconstruction which only requires a small number of linear algebra steps. It is therefore much faster than the iterative method used by Idier et al. We also propose a new representation of the imaged object based on Dirac delta expansion functions.

Stochastic Gradient Langevin Dynamics with Variance Reduction

Stochastic gradient Langevin dynamics (SGLD) has gained the attention of optimization researchers due to its global optimization properties. This paper proves an improved convergence property to local minimizers of nonconvex objective functions using SGLD accelerated by variance reductions. Moreover, we prove an ergodicity property of the SGLD scheme, which gives insights on its potential to find global minimizers of nonconvex objectives.

Modeling massive multivariate spatial data with the basis graphical lasso

We propose a new modeling framework for highly multivariate spatial processes that synthesizes ideas from recent multiscale and spectral approaches with graphical models. The basis graphical lasso writes a univariate Gaussian process as a linear combination of basis functions weighted with entries of a Gaussian graphical vector whose graph is estimated from optimizing an $\ell_1$ penalized likelihood. This paper extends the setting to a multivariate Gaussian process where the basis functions are weighted with Gaussian graphical vectors. We motivate a model where the basis functions represent different levels of resolution and the graphical vectors for each level are assumed to be independent. Using an orthogonal basis grants linear complexity and memory usage in the number of spatial locations, the number of basis functions, and the number of realizations. An additional fusion penalty encourages a parsimonious conditional independence structure in the multilevel graphical model. We illustrate our method on a large climate ensemble from the National Center for Atmospheric Research's Community Atmosphere Model that involves 40 spatial processes.

Spectral estimation from simulations via sketching

Sketching is a stochastic dimension reduction method that preserves geometric structures of data and has applications in high-dimensional regression, low rank approximation and graph sparsification. In this work, we show that sketching can be used to compress simulation data and still accurately estimate time autocorrelation and power spectral density. For a given compression ratio, the accuracy is much higher than using previously known methods. In addition to providing theoretical guarantees, we apply sketching to a molecular dynamics simulation of methanol and find that the estimate of spectral density is 90% accurate using only 10% of the data.