With the rapid growth of neuroimaging technologies, a great effort has been dedicated recently to investigate the dynamic changes in brain activity. Examples include time course calcium imaging and dynamic brain functional connectivity. In this paper, we propose a novel nonparametric matrix response regression model to characterize the nonlinear association between 2D image outcomes and predictors such as time and patient information. Our estimation procedure can be formulated as a nuclear norm regularization problem, which can capture the underlying low-rank structure of the dynamic 2D images. We present a computationally efficient algorithm, derive the asymptotic theory, and show that the method outperforms other existing approaches in simulations. We then apply the proposed method to a calcium imaging study for estimating the change of fluorescent intensities of neurons, and an electroencephalography study for a comparison in the dynamic connectivity covariance matrices between alcoholic and control individuals. For both studies, the method leads to a substantial improvement in prediction error.

中文翻译：

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应用于脑成像数据分析的非参数矩阵响应回归

随着神经影像技术的快速发展，最近人们致力于研究大脑活动的动态变化。例子包括时程钙成像和动态大脑功能连接。在本文中，我们提出了一种新的非参数矩阵响应回归模型来表征二维图像结果与预测因子（如时间和患者信息）之间的非线性关联。我们的估计过程可以表述为核范数正则化问题，它可以捕获动态二维图像的底层低秩结构。我们提出了一种计算效率高的算法，推导出渐近理论，并表明该方法在模拟中优于其他现有方法。然后，我们将所提出的方法应用于钙成像研究以估计神经元荧光强度的变化，以及脑电图研究以比较酒精和控制个体之间的动态连接协方差矩阵。对于这两项研究，该方法都可以显着改善预测误差。