Ultrasound image quality has been continually improving. However, when needles or other metallic objects are operating inside the tissue, the resulting reverberation artifacts can severely corrupt the surrounding image quality. Such effects are challenging for existing computer vision algorithms for medical image analysis. Needle reverberation artifacts can be hard to identify at times and affect various pixel values to different degrees. The boundaries of such artifacts are ambiguous, leading to disagreement among human experts labeling the artifacts. We purpose a weakly- and semi-supervised, probabilistic needle-and-needle-artifact segmentation algorithm to separate the desired tissue-based pixel values from the superimposed artifacts. Our method models the intensity decay of artifact intensities and is designed to minimize the human labeling error. We demonstrate the applicability of the approach, comparing it against other segmentation algorithms. Our method is capable of differentiating the reverberations from artifact-free patches between reverberations, as well as modeling the intensity fall-off in the artifacts. Our method matches state-of-the-art artifact segmentation performance, and sets a new standard in estimating the per-pixel contributions of artifact vs underlying anatomy, especially in the immediately adjacent regions between reverberation lines.