Minimizing the need for pixel-level annotated data for training PET anomaly segmentation networks is crucial, particularly due to time and cost constraints related to expert annotations. Current un-/weakly-supervised anomaly detection methods rely on autoencoder or generative adversarial networks trained only on healthy data, although these are more challenging to train. In this work, we present a weakly supervised and Implicitly guided COuNterfactual diffusion model for Detecting Anomalies in PET images, branded as IgCONDA-PET. The training is conditioned on image class labels (healthy vs. unhealthy) along with implicit guidance to generate counterfactuals for an unhealthy image with anomalies. The counterfactual generation process synthesizes the healthy counterpart for a given unhealthy image, and the difference between the two facilitates the identification of anomaly locations. The code is available at: https://github.com/igcondapet/IgCONDA-PET.git

Automated slice classification is clinically relevant since it can be incorporated into medical image segmentation workflows as a preprocessing step that would flag slices with a higher probability of containing tumors, thereby directing physicians' attention to the important slices. In this work, we train a ResNet-18 network to classify axial slices of lymphoma PET/CT images (collected from two institutions) depending on whether the slice intercepted a tumor (positive slice) in the 3D image or if the slice did not (negative slice). Various instances of the network were trained on 2D axial datasets created in different ways: (i) slice-level split and (ii) patient-level split; inputs of different types were used: (i) only PET slices and (ii) concatenated PET and CT slices; and different training strategies were employed: (i) center-aware (CAW) and (ii) center-agnostic (CAG). Model performances were compared using the area under the receiver operating characteristic curve (AUROC) and the area under the precision-recall curve (AUPRC), and various binary classification metrics. We observe and describe a performance overestimation in the case of slice-level split as compared to the patient-level split training. The model trained using patient-level split data with the network input containing only PET slices in the CAG training regime was the best performing/generalizing model on a majority of metrics. Our models were additionally more closely compared using the sensitivity metric on the positive slices from their respective test sets.

This study performs comprehensive evaluation of four neural network architectures (UNet, SegResNet, DynUNet, and SwinUNETR) for lymphoma lesion segmentation from PET/CT images. These networks were trained, validated, and tested on a diverse, multi-institutional dataset of 611 cases. Internal testing (88 cases; total metabolic tumor volume (TMTV) range [0.52, 2300] ml) showed SegResNet as the top performer with a median Dice similarity coefficient (DSC) of 0.76 and median false positive volume (FPV) of 4.55 ml; all networks had a median false negative volume (FNV) of 0 ml. On the unseen external test set (145 cases with TMTV range: [0.10, 2480] ml), SegResNet achieved the best median DSC of 0.68 and FPV of 21.46 ml, while UNet had the best FNV of 0.41 ml. We assessed reproducibility of six lesion measures, calculated their prediction errors, and examined DSC performance in relation to these lesion measures, offering insights into segmentation accuracy and clinical relevance. Additionally, we introduced three lesion detection criteria, addressing the clinical need for identifying lesions, counting them, and segmenting based on metabolic characteristics. We also performed expert intra-observer variability analysis revealing the challenges in segmenting ``easy'' vs. ``hard'' cases, to assist in the development of more resilient segmentation algorithms. Finally, we performed inter-observer agreement assessment underscoring the importance of a standardized ground truth segmentation protocol involving multiple expert annotators. Code is available at: https://github.com/microsoft/lymphoma-segmentation-dnn

This paper presents a general framework for norm-based capacity control for $L_{p,q}$ weight normalized deep neural networks. We establish the upper bound on the Rademacher complexities of this family. With an $L_{p,q}$ normalization where $q\le p^*$ and $1/p+1/p^{*}=1$, we discuss properties of a width-independent capacity control, which only depends on the depth by a square root term. We further analyze the approximation properties of $L_{p,q}$ weight normalized deep neural networks. In particular, for an $L_{1,\infty}$ weight normalized network, the approximation error can be controlled by the $L_1$ norm of the output layer, and the corresponding generalization error only depends on the architecture by the square root of the depth.

This paper presents a general framework for norm-based capacity control for $L_{p,q}$ weight normalized deep neural networks. We establish the upper bound on the Rademacher complexities of this family. With an $L_{p,q}$ normalization where $q\le p^*$ and $1/p+1/p^{*}=1$, we discuss properties of a width-independent capacity control, which only depends on the depth by a square root term. We further analyze the approximation properties of $L_{p,q}$ weight normalized deep neural networks. In particular, for an $L_{1,\infty}$ weight normalized network, the approximation error can be controlled by the $L_1$ norm of the output layer, and the corresponding generalization error only depends on the architecture by the square root of the depth.

This paper presents a general framework for norm-based capacity control for $L_{p,q}$ weight normalized deep neural networks. We establish the upper bound on the Rademacher complexities of this family. With an $L_{p,q}$ normalization where $q\le p^*$, and $1/p+1/p^{*}=1$, we discuss properties of a width-independent capacity control, which only depends on depth by a square root term. We further analyze the approximation properties of $L_{p,q}$ weight normalized deep neural networks. In particular, for an $L_{1,\infty}$ weight normalized network, the approximation error can be controlled by the $L_1$ norm of the output layer, and the corresponding generalization error only depends on the architecture by the square root of the depth.

In this paper, we propose a compositional nonparametric method in which a model is expressed as a labeled binary tree of $2k+1$ nodes, where each node is either a summation, a multiplication, or the application of one of the $q$ basis functions to one of the $p$ covariates. We show that in order to recover a labeled binary tree from a given dataset, the sufficient number of samples is $O(k\log(pq)+\log(k!))$, and the necessary number of samples is $\Omega(k\log (pq)-\log(k!))$. We further propose a greedy algorithm for regression in order to validate our theoretical findings through synthetic experiments.