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We investigate a numerical method for approximating the solution of the one dimensional acoustic wave problem, when violating the numerical stability condition. We use deep learning to create an explicit non-linear scheme that remains stable for larger time steps and produces better accuracy than the reference implicit method. The proposed spatio-temporal neural-network architecture is additionally enhanced during training with a physically-informed term, adapting it to the physical problem it is approximating and thus more accurate.

One of the main challenges in computed tomography (CT) is how to balance between the amount of radiation the patient is exposed to during scan time and the quality of the reconstructed CT image. We propose a mathematical model for adaptive CT sensing whose goal is to reduce dosage levels while maintaining high image quality at the same time. The adaptive algorithm iterates between selective limited sensing and improved reconstruction, with the goal of applying only the dose level required for sufficient image quality. The theoretical foundation of the algorithm is nonlinear Ridgelet approximation and a discrete form of Ridgelet analysis is used to compute the selective acquisition steps that best capture the image edges. We show experimental results where for the same number of line projections, the adaptive model produces higher image quality, when compared with standard limited angle, nonadaptive sensing algorithms.

This paper considers the problem of estimating the delays of a weighted superposition of pulses, called stream of pulses, in a noisy environment. We show that the delays can be estimated using a tractable convex optimization problem with a localization error proportional to the square root of the noise level. Furthermore, all false detections produced by the algorithm have small amplitudes. Numerical and in-vitro ultrasound experiments corroborate the theoretical results and demonstrate their applicability for the ultrasound imaging signal processing.

We model the inverse physical problem of identifying an underwater obstacle by using the acoustic wave equation. Measurements are collected in a set of sensors placed in the medium. We use this partial information to approximate a segmentation of the obstacle in its correct location. This is an ill-posed problem. We propose a novel deep learning architecture that takes as input the sensor data and computes an approximate segmentation map of the obstacle.

Digital pathology diagnostics are often based on subjective qualitative measures. A murine model of early-phase pancreatic ductal adenocarcinoma provides a controlled environment with a priori knowledge of the genetic mutation and stage of the disease. Use of this model enables the application of supervised learning methods to digital pathology. A computerized diagnostics system for histological detection of pancreatic adenocarcinoma was developed and tested. METHODS : Pathological HE-stained specimens with early pancreatic lesions were identified and evaluated with a system that models cancer detection using a top-down object learning paradigm, mimicking the way a pathologist learns. First, the dominant primitives were identified and segmented in the images, i.e., the ducts, nuclei and tumor stroma. A boost-based machine learning technique was used for duct segmentation, classification and outlier pruning. Second, a set of morphological features traditionally used for cancer diagnosis which provides quantitative image features was employed to quantify subtle findings such as duct deformation and nuclei malformations. Finally, a visually interpretable predictive model was trained to distinguish between normal tissue and premalignant cancer lesions, given ground truth samples. RESULTS : A predictive success rate of 92% was achieved using tenfold cross-validation and 93% on an independent test set. Comparison was made with state-of-the-art classification algorithms that are not interpretable as visible features yielded the contribution of individual primitive features to the prediction outcome.Quantitative image analysis and classification were successful in preclinical histology diagnosis for early-stage pancreatic adenocarcinoma. The usage of annotated contours coupled with interpretable supervised learning methods and outlier pruning can be adapted to other medical imaging tasks. The usage of interpretable supervised learning techniques may improve the success of CAD in histopathological diagnosis.

In recent years, the theory of compressed sensing has emerged as an alternative for the Shannon sampling theorem, suggesting that compressible signals can be reconstructed from far fewer samples than required by the Shannon sampling theorem. In fact the theory advocates that nonadaptive, “random” functionals are in some sense optimal for this task. However, in practice, compressed sensing is very difficult to implement for large data sets, particularly because the recovery algorithms require significant computational resources. In this work, we present a new alternative method for simultaneous image acquisition and compression called adaptive compressed sampling. We exploit wavelet tree structures found in natural images to replace the “universal” acquisition of incoherent measurements with a direct and fast method for adaptive wavelet tree acquisition. The main advantages of this direct approach are that no complex recovery algorithm is in fact needed and that it allows more control over the compressed image quality, in particular, the sharpness of edges. Our experimental results show, by way of software simulations, that our adaptive algorithms perform better than existing nonadaptive methods in terms of image quality and speed.

One of the main challenges in Computed Tomography is to balance the amount of radiation exposure to the patient at the time of the scan with high image quality. We propose a mathematical model for adaptive Computed Tomography acquisition whose goal is to reduce dosage levels while maintaining high image quality at the same time. The adaptive algorithm iterates between selective limited acquisition and improved reconstruction, with the goal of applying only the dose level needed for sufficient image quality. The theoretical foundation of the algorithm is nonlinear Ridgelet approximation and a discrete form of Ridgelet analysis is used to compute the selective acquisition steps that best capture the image edges. We show experimental results where the adaptive model produces significantly higher image quality, when compared with known non-adaptive acquisition algorithms, for the same number of projection lines.

One of the main challenges in Computed Tomography (CT) is how to balance between the amount of radiation the patient is exposed to during scan time and the quality of the CT image. We propose a mathematical model for adaptive CT acquisition whose goal is to reduce dosage levels while maintaining high image quality at the same time. The adaptive algorithm iterates between selective limited acquisition and improved reconstruction, with the goal of applying only the dose level required for sufficient image quality. The theoretical foundation of the algorithm is nonlinear Ridgelet approximation and a discrete form of Ridgelet analysis is used to compute the selective acquisition steps that best capture the image edges. We show experimental results where for the same number of line projections, the adaptive model produces higher image quality, when compared with standard limited angle, non-adaptive acquisition algorithms.

We present an algorithm for highly geometric sparse representation. The algorithm combines the adaptive Geometric Wavelets method with the Active Contour segmentation to overcome limitations of both algorithms. It generalizes the Geometric Wavelets by allowing to adaptively construct wavelets supported on curved domains. It also improves upon the Active Contour method that can only be used to segment a limited number of objects. We show applications of this new method in medical image segmentation.