The field of medical image reconstruction has seen roughly four types of
methods. The first type tended to be analytical methods, such as filtered
back-projection (FBP) for X-ray computed tomography (CT) and the inverse
Fourier transform for magnetic resonance imaging (MRI), based on simple
mathematical models for the imaging systems. These methods are typically fast,
but have suboptimal properties such as poor resolution-noise trade-off for CT.
A second type is iterative reconstruction methods based on more complete models
for the imaging system physics and, where appropriate, models for the sensor
statistics. These iterative methods improved image quality by reducing noise
and artifacts. The FDA-approved methods among these have been based on
relatively simple regularization models. A third type of methods has been
designed to accommodate modified data acquisition methods, such as reduced
sampling in MRI and CT to reduce scan time or radiation dose. These methods
typically involve mathematical image models involving assumptions such as
sparsity or low-rank. A fourth type of methods replaces mathematically designed
models of signals and systems with data-driven or adaptive models inspired by
the field of machine learning. This paper focuses on the two most recent trends
in medical image reconstruction: methods based on sparsity or low-rank models,
and data-driven methods based on machine learning techniques.

本文介绍了医学图像重建方法中的四种类型，并聚焦于近期发展起来的基于稀疏性或低秩模型、以及基于机器学习技术的数据驱动方法。

图像重建：从稀疏性到数据自适应方法和机器学习

Image Reconstruction: From Sparsity to Data-adaptive Methods and Machine  Learning

Subsampled blind deconvolution is the recovery of two unknown signals from
samples of their convolution. To overcome the ill-posedness of this problem,
solutions based on priors tailored to specific application have been developed
in practical applications. In particular, sparsity models have provided
promising priors. However, in spite of empirical success of these methods in
many applications, existing analyses are rather limited in two main ways: by
disparity between the theoretical assumptions on the signal and/or measurement
model versus practical setups; or by failure to provide a performance guarantee
for parameter values within the optimal regime defined by the information
theoretic limits. In particular, it has been shown that a naive sparsity model
is not a strong enough prior for identifiability in the blind deconvolution
problem. Instead, in addition to sparsity, we adopt a conic constraint, which
enforces spectral flatness of the signals. Under this prior, we provide an
iterative algorithm that achieves guaranteed performance in blind deconvolution
at near optimal sample complexity. Numerical results show the empirical
performance of the iterative algorithm agrees with the performance guarantee.

本文提出了一种基于稀疏模型和锥约束的迭代算法，以实现盲卷积问题中的性能保证。在这个先验的基础上，该算法在接近最优样本复杂度的情况下实现了盲卷积问题的拟合精度。

从子采样卷积中盲恢复稀疏信号

Blind Recovery of Sparse Signals from Subsampled Convolution

Recent studies have demonstrated advantages of information fusion based on
sparsity models for multimodal classification. Among several sparsity models,
tree-structured sparsity provides a flexible framework for extraction of
cross-correlated information from different sources and for enforcing group
sparsity at multiple granularities. However, the existing algorithm only solves
an approximated version of the cost functional and the resulting solution is
not necessarily sparse at group levels. This paper reformulates the
tree-structured sparse model for multimodal classification task. An accelerated
proximal algorithm is proposed to solve the optimization problem, which is an
efficient tool for feature-level fusion among either homogeneous or
heterogeneous sources of information. In addition, a (fuzzy-set-theoretic)
possibilistic scheme is proposed to weight the available modalities, based on
their respective reliability, in a joint optimization problem for finding the
sparsity codes. This approach provides a general framework for quality-based
fusion that offers added robustness to several sparsity-based multimodal
classification algorithms. To demonstrate their efficacy, the proposed methods
are evaluated on three different applications - multiview face recognition,
multimodal face recognition, and target classification.

本研究针对多模态分类任务，重新建立了基于树形稀疏模型的优化模型，并提出了一种加速的近端算法，以便高效地实现均质或异质信息源的特征级融合。同时，基于模态可靠性权重的特定模糊集理论，提出了一种算法用于联合优化问题，寻找稀疏编码，从而提供了一种基于质量的融合框架，从而提高了几种基于稀疏模型的多模态分类算法的鲁棒性。最后，本文在三个不同的应用场景下验证了该方法的有效性：多视角人脸识别，多模态人脸识别和目标分类。