Computational imaging has been revolutionized by compressed sensing algorithms, which offer guaranteed uniqueness, convergence, and stability properties. In recent years, model-based deep learning methods that combine imaging physics with learned regularization priors have been emerging as more powerful alternatives for image recovery. The main focus of this paper is to introduce a memory efficient model-based algorithm with similar theoretical guarantees as CS methods. The proposed iterative algorithm alternates between a gradient descent involving the score function and a conjugate gradient algorithm to encourage data consistency. The score function is modeled as a monotone convolutional neural network. Our analysis shows that the monotone constraint is necessary and sufficient to enforce the uniqueness of the fixed point in arbitrary inverse problems. In addition, it also guarantees the convergence to a fixed point, which is robust to input perturbations. Current algorithms including RED and MoDL are special cases of the proposed algorithm; the proposed theoretical tools enable the optimization of the framework for the deep equilibrium setting. The proposed deep equilibrium formulation is significantly more memory efficient than unrolled methods, which allows us to apply it to 3D or 2D+time problems that current unrolled algorithms cannot handle.

我们为高分辨率自由呼吸肺MRI介绍了无监督的运动补偿重建方案。我们将时间序列中的图像帧模拟为3D模板图像卷的变形版本。我们假设变形图在高维空间中的光滑歧管上是点。具体地，我们在每次时刻模拟变形图作为基于CNN的发电机的输出，该发电机的输出具有由低维潜航向量驱动的所有时间框架的权重。潜伏向量的时间序列占数据集中的动态，包括呼吸运动和散装运动。模板图像卷，发电机的参数，以及潜在矢量的直接从k-t空间数据以无监督的方式学习。我们的实验结果表明，与最先进的方法相比，改进了重建，特别是在扫描期间散装运动的背景下。

基于模型的深度学习（MODL）依赖展开的算法是作为图像恢复的强大工具。在这项工作中，我们介绍了一种新颖的单调运营商学习框架，以克服与当前展开框架相关的一些挑战，包括高记忆成本，缺乏对扰动的鲁布利的保证，以及低的可解释性。与使用有限数量迭代的展开架构不同，我们使用深度均衡（DEQ）框架来迭代算法来收敛，并使用Jacobian迭代评估卷积神经网络块的梯度。这种方法显着降低了内存需求，促进了ModL算法的扩展到高维问题。我们将CNN限制为单调运算符，允许我们引入具有保证收敛性的算法和鲁棒性保证。我们在平行MRI的背景下展示了所提出的方案的效用。

依赖广泛训练数据的深度学习算法正在彻底改变图像恢复从令人虐待的测量。在许多成像应用中，培训数据稀缺，包括超高分辨率成像。引入了用于单次图像恢复的深图（DIP）算法，完全消除了对训练数据的需求。利用该方案的挑战是需要早期停止以最小化CNN参数的过度，以对测量中的噪声最小化。我们介绍了一般性的Stein的无偏见风险估计（GSURE）损失度量，以最大限度地减少过度装备。我们的实验表明，确定的方法最大限度地减少了过度装备的问题，从而提高了古典DIP方案的显着提高的性能。我们还使用CuSt-DIP方法与基于模型的展开架构，其通过直接反转方案提供了改进的性能。

自由呼吸的心脏MRI计划是呼吸持有的Cine MRI协议的竞争替代方案，使适用于儿科和其他不能屏住呼吸的人群。因为来自切片的数据顺序获取，所以心脏/呼吸运动模式可能对每个切片不同;目前的自由呼吸方法对每个切片进行独立恢复。除了不能利用切片间冗余之外，需要手动干预或复杂的后处理方法来对准恢复后的图像进行量化。为了克服这些挑战，我们提出了一种无监督的变分深歧管学习方案，用于多层动态MRI的联合对准和重建。该方案共同了解深网络的参数以及捕获特定对象的K-T空间数据的运动引起的动态变化的每个切片的潜在矢量。变形框架最小化表示中的非唯一性，从而提供改进的对准和重建。

我们介绍了一种无监督的深层歧管学习算法，用于运动补偿动态MRI。我们假设自由呼吸的肺部MRI数据集中的运动场在歧管上。每次即时的运动场被建模为深生成模型的输出，由捕获时间变异性的低维时变潜沿驱动。每次即时的图像都是使用上述运动字段作为图像模板的变形版本的建模。模板，深发电机的参数，以及潜伏向量以无监督的方式从K-T空间数据中学到。歧管运动模型用作规范器，使得运动场和图像的联合估计来自少数径向辐射/帧井井出良好。在运动补偿的高分辨率肺线MRI的背景下证明了算法的效用。

Image reconstruction using deep learning algorithms offers improved reconstruction quality and lower reconstruction time than classical compressed sensing and model-based algorithms. Unfortunately, clean and fully sampled ground-truth data to train the deep networks is often unavailable in several applications, restricting the applicability of the above methods. We introduce a novel metric termed the ENsemble Stein's Unbiased Risk Estimate (ENSURE) framework, which can be used to train deep image reconstruction algorithms without fully sampled and noise-free images. The proposed framework is the generalization of the classical SURE and GSURE formulation to the setting where the images are sampled by different measurement operators, chosen randomly from a set. We evaluate the expectation of the GSURE loss functions over the sampling patterns to obtain the ENSURE loss function. We show that this loss is an unbiased estimate for the true mean-square error, which offers a better alternative to GSURE, which only offers an unbiased estimate for the projected error. Our experiments show that the networks trained with this loss function can offer reconstructions comparable to the supervised setting. While we demonstrate this framework in the context of MR image recovery, the ENSURE framework is generally applicable to arbitrary inverse problems.

Biological systems and processes are networks of complex nonlinear regulatory interactions between nucleic acids, proteins, and metabolites. A natural way in which to represent these interaction networks is through the use of a graph. In this formulation, each node represents a nucleic acid, protein, or metabolite and edges represent intermolecular interactions (inhibition, regulation, promotion, coexpression, etc.). In this work, a novel algorithm for the discovery of latent graph structures given experimental data is presented.

The Government of Kerala had increased the frequency of supply of free food kits owing to the pandemic, however, these items were static and not indicative of the personal preferences of the consumers. This paper conducts a comparative analysis of various clustering techniques on a scaled-down version of a real-world dataset obtained through a conjoint analysis-based survey. Clustering carried out by centroid-based methods such as k means is analyzed and the results are plotted along with SVD, and finally, a conclusion is reached as to which among the two is better. Once the clusters have been formulated, commodities are also decided upon for each cluster. Also, clustering is further enhanced by reassignment, based on a specific cluster loss threshold. Thus, the most efficacious clustering technique for designing a food kit tailored to the needs of individuals is finally obtained.

Over the past decade, neural networks have been successful at making predictions from biological sequences, especially in the context of regulatory genomics. As in other fields of deep learning, tools have been devised to extract features such as sequence motifs that can explain the predictions made by a trained network. Here we intend to go beyond explainable machine learning and introduce SEISM, a selective inference procedure to test the association between these extracted features and the predicted phenotype. In particular, we discuss how training a one-layer convolutional network is formally equivalent to selecting motifs maximizing some association score. We adapt existing sampling-based selective inference procedures by quantizing this selection over an infinite set to a large but finite grid. Finally, we show that sampling under a specific choice of parameters is sufficient to characterize the composite null hypothesis typically used for selective inference-a result that goes well beyond our particular framework. We illustrate the behavior of our method in terms of calibration, power and speed and discuss its power/speed trade-off with a simpler data-split strategy. SEISM paves the way to an easier analysis of neural networks used in regulatory genomics, and to more powerful methods for genome wide association studies (GWAS).