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This paper proposes a new convolutional neural network with multiscale processing for detecting ground-glass opacity (GGO) nodules in 3D computed tomography (CT) images, which is referred to as PiaNet for short. PiaNet consists of a feature-extraction module and a prediction module. The former module is constructed by introducing pyramid multiscale source connections into a contracting-expanding structure. The latter module includes a bounding-box regressor and a classifier that are employed to simultaneously recognize GGO nodules and estimate bounding boxes at multiple scales. To train the proposed PiaNet, a two-stage transfer learning strategy is developed. In the first stage, the feature-extraction module is embedded into a classifier network that is trained on a large data set of GGO and non-GGO patches, which are generated by performing data augmentation from a small number of annotated CT scans. In the second stage, the pretrained feature-extraction module is loaded into PiaNet, and then PiaNet is fine-tuned using the annotated CT scans. We evaluate the proposed PiaNet on the LIDC-IDRI data set. The experimental results demonstrate that our method outperforms state-of-the-art counterparts, including the Subsolid CAD and Aidence systems and S4ND and GA-SSD methods. PiaNet achieves a sensitivity of 91.75% with only one false positive per scan

The popular softmax loss and its recent extensions have achieved great success in the deep learning-based image classification. However, the data for training image classifiers usually has different quality. Ignoring such problem, the correct classification of low quality data is hard to be solved. In this paper, we discover the positive correlation between the feature norm of an image and its quality through careful experiments on various applications and various deep neural networks. Based on this finding, we propose a contraction mapping function to compress the range of feature norms of training images according to their quality and embed this contraction mapping function into softmax loss or its extensions to produce novel learning objectives. The experiments on various classification applications, including handwritten digit recognition, lung nodule classification, face verification and face recognition, demonstrate that the proposed approach is promising to effectively deal with the problem of learning on the data with different quality and leads to the significant and stable improvements in the classification accuracy.

Automatic segmentation of liver tumors in medical images is crucial for the computer-aided diagnosis and therapy. It is a challenging task, since the tumors are notoriously small against the background voxels. This paper proposes a new three-stage curriculum learning approach for training deep networks to tackle this small object segmentation problem. The learning in the first stage is performed on the whole input to obtain an initial deep network for tumor segmenta-tion. Then the second stage of learning focuses the strength-ening of tumor specific features by continuing training the network on the tumor patches. Finally, we retrain the net-work on the whole input in the third stage, in order that the tumor specific features and the global context can be inte-grated ideally under the segmentation objective. Benefitting from the proposed learning approach, we only need to em-ploy one single network to segment the tumors directly. We evaluated our approach on the 2017 MICCAI Liver Tumor Segmentation challenge dataset. In the experiments, our approach exhibits significant improvement compared with the commonly used cascaded counterpart., Comment: 5 pages, 3 figures, 1 table, conference

Suppose that $X\_{1}$ and $X\_{2}$ are two selfadjoint random variables that are freely independent over an operator algebra $\mathcal{B}$. We describe the possible operator atoms of the distribution of $X\_{1}+X\_{2}$ and, using linearization, we determine the possible eigenvalues of an arbitrary polynomial $p(X\_{1},X\_{2})$ in case $\mathcal{B}=\mathbb{C}$., Comment: Second version, major modifications. Comments most welcome

We study $N$-ary non-commutative notions of independence, which are given by trees and which generalize free, Boolean, and monotone independence. For every rooted subtree $\mathcal{T}$ of the $N$-regular tree, we define the $\mathcal{T}$-free product of $N$ non-commutative probability spaces and we define the $\mathcal{T}$-free additive convolution of $N$ non-commutative laws. These $N$-ary convolution operations form a topological symmetric operad which includes the free, Boolean, monotone, and anti-monotone convolutions, as well as the orthogonal and subordination convolutions. Using the operadic framework, the proof of convolution identities (such as the relation between free, monotone, and subordination convolutions studied by Lenczewski) can be reduced to combinatorial manipulations of trees. We also develop a theory of $\mathcal{T}$-free independence that closely parallels the free, Boolean, and monotone cases, provided that the root vertex has more than one neighbor. In particular, we study the case where the root vertex of $\mathcal{T}$ has $n$ children and each other vertex has $d$ children, and we relate the $\mathcal{T}$-free convolution powers to free and Boolean convolution powers and the Belinschi-Nica semigroup., Comment: 114 pages, 3 figures, updated with newer references and more examples