<p>Matrix-valued data have found extensive applications in various fields, such as modern biomedical imaging, chemometrics, and economics. In this paper, we address the problem of generalized trace regression involving matrix-valued covariates. To estimate the unknown parameters, we propose a penalty that combines the MCP nuclear norm and two-dimensional spline lasso. This penalty accounts for the potential low-rank and row/column order structures in the matrix-valued covariates. We establish the general theory and explicit statistical convergence rate of the resulting estimator. Through simulations, we demonstrate the advantages of our proposed method compared to other competing methods. Finally, we apply our approach to analyze the brain-image datasets related to Alzheimer’s disease, identifying several efficient regions that illustrate the mechanism of Alzheimer.</p>