We study the problem of subspace tracking in the presence of missing data (ST-miss). In recent work, we studied a related problem called robust ST. In this work, we show that a simple modification of our robust ST solution also provably solves ST-miss and robust ST-miss. To our knowledge, our result is the first "complete" guarantee for ST-miss. This means that we can prove that under assumptions on only the algorithm inputs, the output subspace estimates are close to the true data subspaces at all times. Our guarantees hold under mild and easily interpretable assumptions, and allow the underlying subspace to change with time in a piecewise constant fashion. In contrast, all existing guarantees for ST are partial results and assume a fixed unknown subspace. Extensive numerical experiments are shown to back up our theoretical claims. Finally, our solution can be interpreted as a provably correct mini-batch and memoryefficient solution to low rank Matrix Completion (MC).
Narrow-band imaging (NBI) is an advanced bronchoscopic technique that has shown much potential in the early detection and staging of lung cancer. NBI offers enhanced visualization of microvascular structures and mucosal morphology in the epithelium (airway walls) that are hallmarks of neoplasia. Recent studies suggest that these lesions are helpful in predicting the histological structure of the epithelial tissue in the early stages of lung cancer. Moreover, studies show a strong correlation between the invasiveness of a lesion and its vascular patterns. Shibuya first described these pathological patterns on bronchial mucosa in order to differentiate between specific histological stages of lung cancer. We propose a method to identify these vascular patterns to provide physicians with information that can later be used to sample bronchial abnormalities and perform proper histologic studies when suspecting lung cancer. We show that common deep learning based classification methods fail due to the small set of expert-labeled data available for this task. Thus, we propose a few-shot learning approach based on a Siamese network to learn and distinguish the pathological features using a small annotated dataset. Our method demonstrates improved inter-class separation in the embedding space as compared to a baseline CNN classifier model. Furthermore, we achieve an 88% overall classification accuracy on our test dataset, greatly surpassing the baseline model by 31% relative increase in accuracy.
Because radial-probe endobronchial ultrasound (RP-EBUS) can provide real-time confirmation of a suspect peripheral nodule situated outside of the airways, it is widely used during bronchoscopy for lung cancer diagnosis. RP-EBUS, however, tends to be difficult to use effectively, without some form of guidance. Previously, we had prototyped a multimodal image-guided bronchoscopy system that provides guidance during both bronchoscopic navigation and RP-EBUS localization. To use the system, the user first generates a guidance plan offline prior to the live procedure. Later, in the surgical suite, the user then employs the image-guided system to perform the desired multimodal RP-EBUS bronchoscopy, driven by the procedure plan. We now validate this system in a series of live studies. As the first set of end-to-end live system studies, we first tested the system in controlled animal studies. Through these studies, we tested the functionality and feasibility of the system prototype over the standard clinical workflow, without the usual risks associated with live patient procedures. Through these studies, we sharpened the workflow for the prototype and improved user interaction. We then tested the refined system over the standard clinical workflow in our University Hospital's lung cancer management clinic. This study proved the potential of our system for live clinical usage by demonstrating the safety, feasibility, and functionality of our complete system for guiding RP-EBUS bronchoscopy during peripheral nodule diagnosis.
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