A General Approach to Convergence Properties of Some Methods for Nonsmooth Convex Optimization

Based on the notion of the ε -subgradient, we present a unified technique to establish convergence properties of several methods for nonsmooth convex minimization problems. Starting from the technical results, we obtain the global convergence of: (i) the variable metric proximal methods presented by Bonnans, Gilbert, Lemaréchal, and Sagastizábal, (ii) some algorithms proposed by Correa and Lemaréchal, and (iii) the proximal point algorithm given by Rockafellar. In particular, we prove that the Rockafellar—Todd phenomenon does not occur for each of the above mentioned methods. Moreover, we explore the convergence rate of { ||x k || } and {f(x k ) } when {x k } is unbounded and {f(x k ) } is bounded for the non-smooth minimization methods (i), (ii), and (iii).Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/42374/1/245-38-2-141_38n2p141.pd

RCPS: Rectified Contrastive Pseudo Supervision for Semi-Supervised Medical Image Segmentation

Medical image segmentation methods are generally designed as fully-supervised to guarantee model performance, which require a significant amount of expert annotated samples that are high-cost and laborious. Semi-supervised image segmentation can alleviate the problem by utilizing a large number of unlabeled images along with limited labeled images. However, learning a robust representation from numerous unlabeled images remains challenging due to potential noise in pseudo labels and insufficient class separability in feature space, which undermines the performance of current semi-supervised segmentation approaches. To address the issues above, we propose a novel semi-supervised segmentation method named as Rectified Contrastive Pseudo Supervision (RCPS), which combines a rectified pseudo supervision and voxel-level contrastive learning to improve the effectiveness of semi-supervised segmentation. Particularly, we design a novel rectification strategy for the pseudo supervision method based on uncertainty estimation and consistency regularization to reduce the noise influence in pseudo labels. Furthermore, we introduce a bidirectional voxel contrastive loss to the network to ensure intra-class consistency and inter-class contrast in feature space, which increases class separability in the segmentation. The proposed RCPS segmentation method has been validated on two public datasets and an in-house clinical dataset. Experimental results reveal that the proposed method yields better segmentation performance compared with the state-of-the-art methods in semi-supervised medical image segmentation. The source code is available at https://github.com/hsiangyuzhao/RCPS

Uni-COAL: A Unified Framework for Cross-Modality Synthesis and Super-Resolution of MR Images

Cross-modality synthesis (CMS), super-resolution (SR), and their combination (CMSR) have been extensively studied for magnetic resonance imaging (MRI). Their primary goals are to enhance the imaging quality by synthesizing the desired modality and reducing the slice thickness. Despite the promising synthetic results, these techniques are often tailored to specific tasks, thereby limiting their adaptability to complex clinical scenarios. Therefore, it is crucial to build a unified network that can handle various image synthesis tasks with arbitrary requirements of modality and resolution settings, so that the resources for training and deploying the models can be greatly reduced. However, none of the previous works is capable of performing CMS, SR, and CMSR using a unified network. Moreover, these MRI reconstruction methods often treat alias frequencies improperly, resulting in suboptimal detail restoration. In this paper, we propose a Unified Co-Modulated Alias-free framework (Uni-COAL) to accomplish the aforementioned tasks with a single network. The co-modulation design of the image-conditioned and stochastic attribute representations ensures the consistency between CMS and SR, while simultaneously accommodating arbitrary combinations of input/output modalities and thickness. The generator of Uni-COAL is also designed to be alias-free based on the Shannon-Nyquist signal processing framework, ensuring effective suppression of alias frequencies. Additionally, we leverage the semantic prior of Segment Anything Model (SAM) to guide Uni-COAL, ensuring a more authentic preservation of anatomical structures during synthesis. Experiments on three datasets demonstrate that Uni-COAL outperforms the alternatives in CMS, SR, and CMSR tasks for MR images, which highlights its generalizability to wide-range applications

Are intrinsic neural timescales related to sensory processing? Evidence from abnormal behavioral states

The brain exhibits a complex temporal structure which translates into a hierarchy of distinct neural timescales. An open question is how these intrinsic timescales are related to sensory or motor information processing and whether these dynamics have common patterns in different behavioral states. We address these questions by investigating the brain\u27s intrinsic timescales in healthy controls, motor (amyotrophic lateral sclerosis, locked-in syndrome), sensory (anesthesia, unresponsive wakefulness syndrome), and progressive reduction of sensory processing (from awake states over N1, N2, N3). We employed a combination of measures from EEG resting-state data: auto-correlation window (ACW), power spectral density (PSD), and power-law exponent (PLE). Prolonged neural timescales accompanied by a shift towards slower frequencies were observed in the conditions with sensory deficits, but not in conditions with motor deficits. Our results establish that the spontaneous activity\u27s intrinsic neural timescale is related to the neural capacity that specifically supports sensory rather than motor information processing in the healthy brain

Are intrinsic neural timescales related to sensory processing? Evidence from abnormal behavioral states

The brain exhibits a complex temporal structure which translates into a hierarchy of distinct neural timescales. An open question is how these intrinsic timescales are related to sensory or motor information processing and whether these dynamics have common patterns in different behavioral states. We address these questions by investigating the brain\u27s intrinsic timescales in healthy controls, motor (amyotrophic lateral sclerosis, locked-in syndrome), sensory (anesthesia, unresponsive wakefulness syndrome), and progressive reduction of sensory processing (from awake states over N1, N2, N3). We employed a combination of measures from EEG resting-state data: auto-correlation window (ACW), power spectral density (PSD), and power-law exponent (PLE). Prolonged neural timescales accompanied by a shift towards slower frequencies were observed in the conditions with sensory deficits, but not in conditions with motor deficits. Our results establish that the spontaneous activity\u27s intrinsic neural timescale is related to the neural capacity that specifically supports sensory rather than motor information processing in the healthy brain

Are intrinsic neural timescales related to sensory processing? Evidence from abnormal behavioral states

The brain exhibits a complex temporal structure which translates into a hierarchy of distinct neural timescales. An open question is how these intrinsic timescales are related to sensory or motor information processing and whether these dynamics have common patterns in different behavioral states. We address these questions by investigating the brain\u27s intrinsic timescales in healthy controls, motor (amyotrophic lateral sclerosis, locked-in syndrome), sensory (anesthesia, unresponsive wakefulness syndrome), and progressive reduction of sensory processing (from awake states over N1, N2, N3). We employed a combination of measures from EEG resting-state data: auto-correlation window (ACW), power spectral density (PSD), and power-law exponent (PLE). Prolonged neural timescales accompanied by a shift towards slower frequencies were observed in the conditions with sensory deficits, but not in conditions with motor deficits. Our results establish that the spontaneous activity\u27s intrinsic neural timescale is related to the neural capacity that specifically supports sensory rather than motor information processing in the healthy brain

A variant of the Topkis-Veinott method for solving inequality constrained optimization problems

http://deepblue.lib.umich.edu/bitstream/2027.42/3660/5/ban6932.0001.001.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/3660/4/ban6932.0001.001.tx

A unified approach to convergence properties of some methods for nonsmooth convex optimization

http://deepblue.lib.umich.edu/bitstream/2027.42/3659/5/bap9144.0001.001.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/3659/4/bap9144.0001.001.tx

Some methods for solving nonsmooth convex minimization problems J.R. Birge, L. Qi and Z. Wei.

http://deepblue.lib.umich.edu/bitstream/2027.42/3639/5/bbm0223.0001.001.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/3639/4/bbm0223.0001.001.tx