Sparsity via Hyperpriors: A Theoretical and Algorithmic Study under Empirical Bayes Framework

This paper presents a comprehensive analysis of hyperparameter estimation within the empirical Bayes framework (EBF) for sparse learning. By studying the influence of hyperpriors on the solution of EBF, we establish a theoretical connection between the choice of the hyperprior and the sparsity as well as the local optimality of the resulting solutions. We show that some strictly increasing hyperpriors, such as half-Laplace and half-generalized Gaussian with the power in $(0,1)$, effectively promote sparsity and improve solution stability with respect to measurement noise. Based on this analysis, we adopt a proximal alternating linearized minimization (PALM) algorithm with convergence guaranties for both convex and concave hyperpriors. Extensive numerical tests on two-dimensional image deblurring problems demonstrate that introducing appropriate hyperpriors significantly promotes the sparsity of the solution and enhances restoration accuracy. Furthermore, we illustrate the influence of the noise level and the ill-posedness of inverse problems to EBF solutions.

SAM-VMNet: Deep Neural Networks For Coronary Angiography Vessel Segmentation

Coronary artery disease (CAD) is one of the most prevalent diseases in the cardiovascular field and one of the major contributors to death worldwide. Computed Tomography Angiography (CTA) images are regarded as the authoritative standard for the diagnosis of coronary artery disease, and by performing vessel segmentation and stenosis detection on CTA images, physicians are able to diagnose coronary artery disease more accurately. In order to combine the advantages of both the base model and the domain-specific model, and to achieve high-precision and fully-automatic segmentation and detection with a limited number of training samples, we propose a novel architecture, SAM-VMNet, which combines the powerful feature extraction capability of MedSAM with the advantage of the linear complexity of the visual state-space model of VM-UNet, giving it faster inferences than Vision Transformer with faster inference speed and stronger data processing capability, achieving higher segmentation accuracy and stability for CTA images. Experimental results show that the SAM-VMNet architecture performs excellently in the CTA image segmentation task, with a segmentation accuracy of up to 98.32% and a sensitivity of up to 99.33%, which is significantly better than other existing models and has stronger domain adaptability. Comprehensive evaluation of the CTA image segmentation task shows that SAM-VMNet accurately extracts the vascular trunks and capillaries, demonstrating its great potential and wide range of application scenarios for the vascular segmentation task, and also laying a solid foundation for further stenosis detection.

Two New Stenosis Detection Methods of Coronary Angiograms

Coronary angiography is the "gold standard" for diagnosing coronary artery disease (CAD). At present, the methods for detecting and evaluating coronary artery stenosis cannot satisfy the clinical needs, e.g., there is no prior study of detecting stenoses in prespecified vessel segments, which is necessary in clinical practice. Two vascular stenosis detection methods are proposed to assist the diagnosis. The first one is an automatic method, which can automatically extract the entire coronary artery tree and mark all the possible stenoses. The second one is an interactive method. With this method, the user can choose any vessel segment to do further analysis of its stenoses. Experiments show that the proposed methods are robust for angiograms with various vessel structures. The precision, sensitivity, and $F_1$ score of the automatic stenosis detection method are 0.821, 0.757, and 0.788, respectively. Further investigation proves that the interactive method can provide a more precise outcome of stenosis detection, and our quantitative analysis is closer to reality. The proposed automatic method and interactive method are effective and can complement each other in clinical practice. The first method can be used for preliminary screening, and the second method can be used for further quantitative analysis. We believe the proposed solution is more suitable for the clinical diagnosis of CAD.

Two New Stenoses Detection Methods of Coronary Angiograms

Coronary angiography is the "gold standard" for the diagnosis of coronary heart disease. At present, the methods for detecting coronary artery stenoses and evaluating the degree of it in coronary angiograms are either subjective or not efficient enough. Two vascular stenoses detection methods in coronary angiograms are proposed to assist the diagnosis. The first one is an automatic method, which can automatically segment the entire coronary vessels and mark the stenoses. The second one is an interactive method. With this method, the user only needs to give a start point and an end point to detect the stenoses of a certain vascular segment. We have shown that the proposed tracking methods are robust for angiograms with various vessel structure. The automatic detection method can effectively measure the diameter of the vessel and mark the stenoses in different angiograms. Further investigation proves that the results of interactive detection method can accurately reflect the true stenoses situation. The proposed automatic method and interactive method are effective in various angiograms and can complement each other in clinical practice. The first method can be used for preliminary screening and the second method can be used for further quantitative analysis. It has the potential to improve the level of clinical diagnosis of coronary heart disease.