Recently, we have witnessed the success of total variation (TV) for many
imaging applications. However, traditional TV is defined on the original pixel
domain, which limits its potential. In this work, we suggest a new TV
regularization defined on the neural domain. Concretely, the discrete data is
continuously and implicitly represented by a deep neural network (DNN), and we
use the derivatives of DNN outputs w.r.t. input coordinates to capture local
correlations of data. As compared with classical TV on the original domain, the
proposed TV on the neural domain (termed NeurTV) enjoys two advantages. First,
NeurTV is not limited to meshgrid but is suitable for both meshgrid and
non-meshgrid data. Second, NeurTV can more exactly capture local correlations
across data for any direction and any order of derivatives attributed to the
implicit and continuous nature of neural domain. We theoretically reinterpret
NeurTV under the variational approximation framework, which allows us to build
the connection between classical TV and NeurTV and inspires us to develop
variants (e.g., NeurTV with arbitrary resolution and space-variant NeurTV).
Extensive numerical experiments with meshgrid data (e.g., color and
hyperspectral images) and non-meshgrid data (e.g., point clouds and spatial
transcriptomics) showcase the effectiveness of the proposed methods.

在这篇论文中，我们提出了一种在神经领域上定义的新型全变差（TV）正则化方法，通过使用深度神经网络（DNN）输出相对于输入坐标的导数来捕捉数据的局部相关性，实验证明这种方法在不同类型的数据上都非常有效。

NeurTV: 神经领域上的总变差

NeurTV: Total Variation on the Neural Domain

Estimating tissue parameter maps with high accuracy and precision from highly
undersampled measurements presents one of the major challenges in MR
fingerprinting (MRF). Many existing works project the recovered voxel
fingerprints onto the Bloch manifold to improve reconstruction performance.
However, little research focuses on exploiting the latent manifold structure
priors among fingerprints. To fill this gap, we propose a novel MRF
reconstruction framework based on manifold structured data priors. Since it is
difficult to directly estimate the fingerprint manifold structure, we model the
tissue parameters as points on a low-dimensional parameter manifold. We reveal
that the fingerprint manifold shares the same intrinsic topology as the
parameter manifold, although being embedded in different Euclidean spaces. To
exploit the non-linear and non-local redundancies in MRF data, we divide the
MRF data into spatial patches, and the similarity measurement among data
patches can be accurately obtained using the Euclidean distance between the
corresponding patches in the parameter manifold. The measured similarity is
then used to construct the graph Laplacian operator, which represents the
fingerprint manifold structure. Thus, the fingerprint manifold structure is
introduced in the reconstruction framework by using the low-dimensional
parameter manifold. Additionally, we incorporate the locally low-rank prior in
the reconstruction framework to further utilize the local correlations within
each patch for improved reconstruction performance. We also adopt a
GPU-accelerated NUFFT library to accelerate reconstruction in non-Cartesian
sampling scenarios. Experimental results demonstrate that our method can
achieve significantly improved reconstruction performance with reduced
computational time over the state-of-the-art methods.

通过利用流形结构先验信息，我们提出了一种基于重建框架的磁共振指纹成像 (MR fingerprinting) 方法，其中低维参数流形被用来表示指纹流形结构，同时加入局部低秩先验信息以改善重建性能。实验证明，该方法相对于现有方法在重建性能上有显著提升，并且计算时间得到了减少。

基于流形结构数据先验的改进 MR 指纹重建

Exploiting Manifold Structured Data Priors for Improved MR  Fingerprinting Reconstruction

Autoregressive state transitions, where predictions are conditioned on past
predictions, are the predominant choice for both deterministic and stochastic
sequential models. However, autoregressive feedback exposes the evolution of
the hidden state trajectory to potential biases from well-known train-test
discrepancies. In this paper, we combine a latent state space model with a CRF
observation model. We argue that such autoregressive observation models form an
interesting middle ground that expresses local correlations on the word level
but keeps the state evolution non-autoregressive. On unconditional sentence
generation we show performance improvements compared to RNN and GAN baselines
while avoiding some prototypical failure modes of autoregressive models.

本文介绍了一种将潜在状态空间模型与 CRF 观察模型结合的自回归观察模型，在无条件句子生成中，与基线模型相比具有更好的性能，避免了自回归模型的一些典型失败模式。