In the context of lung ultrasound, the detection of B-lines, which are indicative of interstitial lung disease and pulmonary edema, plays a pivotal role in clinical diagnosis. Current methods still rely on visual inspection by experts. Vision-based automatic B-line detection methods have been developed, but their performance has yet to improve in terms of both accuracy and computational speed. This paper presents a novel approach to posing B-line detection as an inverse problem via deep unfolding of the Alternating Direction Method of Multipliers (ADMM). It tackles the challenges of data labelling and model training in lung ultrasound image analysis by harnessing the capabilities of deep neural networks and model-based methods. Our objective is to substantially enhance diagnostic accuracy while ensuring efficient real-time capabilities. The results show that the proposed method runs more than 90 times faster than the traditional model-based method and achieves an F1 score that is 10.6% higher.