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 [Formula: see text] 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 [Formula: see text], [Formula: see text], and [Formula: see text], respectively, and of 24% based on ROC curve evaluations.

Fig. 1.

Line artefacts in lung ultrasound images. B-mode images (top row) and lines overlaid on them (bottom row). There are two, zero and two B-lines in the image on the left, middle and right, respectively. Red, yellow, blue and green lines represent the pleural lines, B-lines, A-lines and Z-lines, respectively.

Fig. 2.

Example of lung ultrasound image (Left column) and its Radon transform (Right column), where the horizontal axis is varying from −45° to 135°, the vertical axis is varying from to , and the brighter intensity indicates higher magnitude of the Radon transform.

Fig. 3.

Block diagram of the proposed automatic B-line detection method.

Fig. 4.

Detected Pleural line (Red) with its estimated location (straight line) and the estimated positions of the A-lines (Green).

Fig. 5.

Simulated ultrasound image. (Left) Line image. (Middle) B-mode image. (Right) Radon transform image with .

Fig. 6.

Results of and () when (top row), (middle row), (bottom row), and (colume 1–2), (colume 3–4), (colume 5–6).

Fig. 7.

Restored lines of the in vivo aerated lung ultrasound images, containing four B-lines (left), using , (middle) and , (right). (Top row) lines in B-mode images. (Bottom row) Radon transform domains.

Fig. 8.

Restored lines when the deblurring is included, using , (left), , (middle), and , (right). (Top row) line positions. (Bottom row) deblurred Radon transform domains.

Fig. 9.

Original B-mode ultrasound image (top row), detected lines (middle row) and Radon transform domain representation of the restored B-mode images using (bottom row). Red, yellow, blue and green lines represent the pleural lines, B-lines, A-lines and Z-lines, respectively.

Fig. 10.

Performance comparison of the B-line identification methods through a receiver operating characteristic curve (ROC curve).