Convolutional neural networks for semantic segmentation suffer from low
performance at object boundaries. In medical imaging, accurate representation
of tissue surfaces and volumes is important for tracking of disease biomarkers
such as tissue morphology and shape features. In this work, we propose a novel
distance map derived loss penalty term for semantic segmentation. We propose to
use distance maps, derived from ground truth masks, to create a penalty term,
guiding the network's focus towards hard-to-segment boundary regions. We
investigate the effects of this penalizing factor against cross-entropy, Dice,
and focal loss, among others, evaluating performance on a 3D MRI bone
segmentation task from the publicly available Osteoarthritis Initiative
dataset. We observe a significant improvement in the quality of segmentation,
with better shape preservation at bone boundaries and areas affected by partial
volume. We ultimately aim to use our loss penalty term to improve the
extraction of shape biomarkers and derive metrics to quantitatively evaluate
the preservation of shape.

本文提出了一种新的距离图生成损失项来辅助卷积神经网络在医学图像分割中选择难以分割区域，经实验证明此项可以显著提高分割质量、更好地保存骨骼边界形状特征，有望用于提取形态学生物标志物，并得出定量评估指标。

语义分割的距离图损失惩罚项

Distance Map Loss Penalty Term for Semantic Segmentation

We investigate leave-one-out cross validation (CV) as a determinator of the
weight of the penalty term in the least absolute shrinkage and selection
operator (LASSO). First, on the basis of the message passing algorithm and a
perturbative discussion assuming that the number of observations is
sufficiently large, we provide simple formulas for approximately assessing two
types of CV errors, which enable us to significantly reduce the necessary cost
of computation. These formulas also provide a simple connection of the CV
errors to the residual sums of squares between the reconstructed and the given
measurements. Second, on the basis of this finding, we analytically evaluate
the CV errors when the design matrix is given as a simple random matrix in the
large size limit by using the replica method. Finally, these results are
compared with those of numerical simulations on finite-size systems and are
confirmed to be correct. We also apply the simple formulas of the first type of
CV error to an actual dataset of the supernovae.

本文利用留一交叉验证的方法，对 LASSO 方法中惩罚项权重的确定进行了研究并提供了两种求解 CV 误差的简单公式，最后将公式应用于超新星实验数据的分析。

LASSO 中的交叉验证及其加速

Cross validation in LASSO and its acceleration

This paper describes performance bounds for compressed sensing (CS) where the
underlying sparse or compressible (sparsely approximable) signal is a vector of
nonnegative intensities whose measurements are corrupted by Poisson noise. In
this setting, standard CS techniques cannot be applied directly for several
reasons. First, the usual signal-independent and/or bounded noise models do not
apply to Poisson noise, which is non-additive and signal-dependent. Second, the
CS matrices typically considered are not feasible in real optical systems
because they do not adhere to important constraints, such as nonnegativity and
photon flux preservation. Third, the typical $\ell_2$--$\ell_1$ minimization
leads to overfitting in the high-intensity regions and oversmoothing in the
low-intensity areas. In this paper, we describe how a feasible positivity- and
flux-preserving sensing matrix can be constructed, and then analyze the
performance of a CS reconstruction approach for Poisson data that minimizes an
objective function consisting of a negative Poisson log likelihood term and a
penalty term which measures signal sparsity. We show that, as the overall
intensity of the underlying signal increases, an upper bound on the
reconstruction error decays at an appropriate rate (depending on the
compressibility of the signal), but that for a fixed signal intensity, the
signal-dependent part of the error bound actually grows with the number of
measurements or sensors. This surprising fact is both proved theoretically and
justified based on physical intuition.

本文提出了一种压缩感知技术的性能边界，并描述了如何构建一个可行的正性和通量保持感知矩阵，以及如何在考虑泊松噪声的情况下进行压缩感知感测数据的重建和信号稀疏度惩罚项的优化。研究表明，在信号整体强度增加时，重建误差的上界以适当的速率下降（取决于信号的可压缩性），但对于固定的信号强度，误差界中的信号相关部分随着测量或传感器数量的增加而增加。