Line Detection as an Inverse Problem: Application to Lung Ultrasound Imaging

Abstract

This paper presents a novel method for line restoration in speckle images. We address this as a sparse estimation problem using both convex and non-convex optimization techniques based on the Radon transform and sparsity regularization. This breaks into subproblems, which are solved using the alternating direction method of multipliers, thereby achieving line detection and deconvolution simultaneously. We include an additional deblurring step in the Radon domain via a total variation blind deconvolution to enhance line visualization and to improve line recognition. We evaluate our approach on a real clinical application: the identification of B-lines in lung ultrasound images. Thus, an automatic B-line identification method is proposed, using a simple local maxima technique in the Radon transform domain, associated with known clinical definitions of line artefacts. Using all initially detected lines as a starting point, our approach then differentiates between B-lines and other lines of no clinical significance, including Z-lines and A-lines. We evaluated our techniques using as ground truth lines identified visually by clinical experts. The proposed approach achieves the best B-line detection performance as measured by the F score when a non-convex \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}$\ell _{\text {p}}$ \end{document} regularization is employed for both line detection and deconvolution. The F scores as well as the receiver operating characteristic (ROC) curves show that the proposed approach outperforms the state-of-the-art methods with improvements in B-line detection performance of 54%, 40%, and 33% for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}${\text {F}}_{0.5}$ \end{document}, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}${\text {F}}_{1}$ \end{document}, and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}${\text {F}}_{2}$ \end{document}, respectively, and of 24% based on ROC curve evaluations.

Automatic Detection of B-Lines in <inline-formula> <tex-math notation="LaTeX">$In Vivo$ </tex-math> </inline-formula> Lung Ultrasound

“…One study compared the Hough transform algorithm with other automated B-line detection techniques [20]. A reduced version of the presented technique by Moshavegh [18] is implemented and used for comparison by Anantrasirichai [20].It implemented the step 3 only, which was the alternate sequential filtering (ASF). Therefore, the comparison was rather based on a partial implementation of the original algorithm.…”

“…The technique analysed the mean and standard deviation of grayscale changes in B-mode images to identify edema. Another study used Hough transform for detcting Blines [20]. The study compared the Hough transform algorithm with other automated techniques, as well as the previously presented technique by authors of this paper in [18].…”

Ship Wake Detection in SAR Images via Sparse Regularization

“…The operator Γ λk (·) in Algorithm 2 is a shrinkage/thresholding/denoising function. In this paper, we used shrinkage/thresholding operators in minimizers with L 1 and L p for Γ λk (·) as also used in [24]…”

“…where prox λk ψk (·) is the Moreau proximal operator for ψ k (·). The soft thresholding operation is the proximal operator for L 1 norm, whereas for L p norm the proximal operator is computed with an iterative algorithm called generalised soft thresholding (GST) [24], [39]. The proximal operator for nuclear norm is obtained via singular value soft thresholding as in [38] and for TV norm it is efficiently computed by using Chambolle's method in [40].…”

Assessment and management of fluid overload in children on dialysis

“…Further work is being undertaken to automate detection of B-lines on ultrasound, with the aim of increasing availability of this technique to patients and carers with limited training requirements [ 32 ].…”