Line Detection as an Inverse Problem – Visual Information Laboratory

In this project, we present a novel method for line artefacts quantification in lung ultrasound (LUS) images of COVID-19 patients. We formulate this as a non-convex regularisation problem involving the heavy-tailed Cauchy-based penalty function, and the inverse Radon transform.

We employ a simple local maxima detection technique in the Radon transform domain, associated with known clinical definitions of line artefacts.

Despite being non-convex, the proposed technique is guaranteed to convergence through our proposed Cauchy proximal splitting (CPS) method, and accurately identifies both horizontal and vertical line artefacts in LUS images. In order to reduce the number of false and missed detection, our method includes a two-stage validation mechanism, which is performed in both Radon and image domains.

We evaluate the performance of the proposed method in comparison to the current state-of-the-art B-line identification method and show a considerable performance gain with 87% correctly detected B-lines in LUS images of nine COVID-19 patients.

Detection results. (a)-(e) Original Images. (f)-(j) Ground truth. (k)-(o) The proposed method.

Further information

[1] Karakuş, O., Anantrasirichai, N., Aguersif, A., Silva, S., Basarab, A., & Achim, A. (2020). Detection of Line Artifacts in Lung Ultrasound Images of COVID-19 Patients Via Nonconvex Regularization. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 67(11), 2218-2229.

Talk

Talk by Dr Oktay Karakus in Acoustics Virtually Everywhere The 179th Meeting of the Acoustical Society of America 7-11 December 2020

https://player.vimeo.com/video/479873161

Contact

Oktay Karakuş, Pui Anantrasirichai, Alin Achim

Code

O Karakus, A Achim. (2020): QuantLUS – CPS v1.0 https://doi.org/10.5523/bris.z47pfkwqivfj2d0qhyq7v3u1i

Funding

This work was supported in part by
** the UK Engineering and Physical Sciences Research Council (EPSRC) under grant EP/R009260/1,
** an EPSRC Impact Acceleration Award (IAA) from the University of Bristol, ** a Leverhulme Trust Research Fellowship to Achim (INFHER).

Example images including ship wakes and their Radon transform. (Upper Left) – Image includes all 5 ship wakes. (Upper Right) – Image does not include Kelvin wake. (Lower row) – Radon transforms of the images above. Both images are TerraSAR-X Stripmap products with HH polarisation and 3m by 3m resolution.

Ship wake detection is essential for extracting information on the wake generating vessels in order to analyse synthetic aperture radar (SAR) images of the sea surface. One possibility is to assume a linear model for wakes, in which case detection approaches are based on transforms such as Radon and Hough. These express the bright (dark) lines as peak (trough) points in the transform domain.

In this project, ship wake detection is posed as an inverse problem, which the associated cost function has taken various forms, such as

** Generalized minimax concave (GMC) function [1,2],
** Non-convex Cauchy-based penalty function [3,4],
** Hybrid penalty function which combines the Cauchy-based penalty with a 2-D DWT based term [5].

Despite having a non-convex regularizer, we provide mathematically consistent solutions, by either

** keeping the overall cost function to be convex [1,2], OR
** setting model parameters to guarantee the convergence [3-5].

To quantify the performance of the proposed methods, various types of SAR images are used, corresponding to TerraSAR-X, COSMO-SkyMed, Sentinel-1, and ALOS2. The performance of various priors in solving the proposed inverse problem is first studied by investigating the GMC along with the L₁, L_p, nuclear and total variation (TV) norms.