Ultrasound images are widespread in medical diagnosis for muscle-skeletal, cardiac, and obstetrical diseases, due to the efficiency and non-invasiveness of the acquisition methodology. However, ultrasound acquisition introduces noise in the signal, which corrupts the resulting image and affects further processing steps, e.g. segmentation and quantitative analysis. We define a novel deep learning framework for the real-time denoising of ultrasound images. Firstly, we compare state-of-the-art methods for denoising (e.g. spectral, low-rank methods) and select WNNM (Weighted Nuclear Norm Minimisation) as the best denoising in terms of accuracy, preservation of anatomical features, and edge enhancement. Then, we propose a tuned version of WNNM (tuned-WNNM) that improves the quality of the denoised images and extends its applicability to ultrasound images. Through a deep learning framework, the tuned-WNNM qualitatively and quantitatively replicates WNNM results in real-time. Finally, our approach is general in terms of its building blocks and parameters of the deep learning and high-performance computing framework; in fact, we can select different denoising algorithms and deep learning architectures.

Ultrasound images are widespread in medical diagnosis for muscleskeletal, cardiac, and obstetrical diseases, due to the efficiency and noninvasiveness of the acquisition methodology. However, ultrasound acquisition introduces a speckle noise in the signal, that corrupts the resulting image and affects further processing operations, and the visual analysis that medical experts conduct to estimate patient diseases. Our main goal is to define a universal deep learning framework for real-time denoising of ultrasound images. We analyse and compare state-of-the-art methods for the smoothing of ultrasound images (e.g., spectral, low-rank, and deep learning denoising algorithms), in order to select the best one in terms of accuracy, preservation of anatomical features, and computational cost. Then, we propose a tuned version of the selected state-of-the-art denoising methods (e.g., WNNM), to improve the quality of the denoised images, and extend its applicability to ultrasound images. To handle large data sets of ultrasound images with respect to applications and industrial requirements, we introduce a denoising framework that exploits deep learning and HPC tools, and allows us to replicate the results of state-of-the-art denoising methods in a real-time execution.

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The denoising of 2D images through low-rank methods is a relevant topic in digital image processing. This paper proposes a novel method that trains a learning network to predict the optimal thresholds of the singular value decomposition involved in the low-rank denoising of 2D images. To improve the denoising results, we apply the block-matching algorithm and classify each 3D block according to four parameters, which increase the specificity of the network for the prediction of the thresholds. Our method outperforms state-of-the-art methods for image denoising; furthermore, it is general with respect to the type of noise and provides an upper bound to the accuracy of the denoising of 2D images through the Singular Value Decomposition.

Partial Differential Equations (PDEs) describe several problems relevant to many fields of applied sciences, and their discrete counterparts typically involve the solution of sparse linear systems. In this context, we focus on the analysis of the computational aspects related to the solution of large and sparse linear systems with HPC solvers, by considering the performances of direct and iterative solvers in terms of computational efficiency, scalability, and numerical accuracy. Our aim is to identify the main criteria to support application-domain specialists in the selection of the most suitable solvers, according to the application requirements and available resources. To this end, we discuss how the numerical solver is affected by the regular/irregular discretisation of the input domain, the discretisation of the input PDE with piecewise linear or polynomial basis functions, which generally result in a higher/lower sparsity of the coefficient matrix, and the choice of different initial conditions, which are associated with linear systems with multiple right-hand side terms. Finally, our analysis is independent of the characteristics of the underlying computational architectures, and provides a methodological approach that can be applied to different classes of PDEs or with approximation problems.