Abstract: Sparse learning-based correlation filtering framework is highly efficient in thermal infrared target tracking, but when the target's appearance changes frequently or is located at the edge of the sampling region, it may introduce false samples and peaks, leading to tracking failure or reduced accuracy. To address this issue, this paper proposes a sparse learning tracking model that combines Tikhonov regularization with a subquadratic penalty term. First, to enhance the model's robustness to noise and interference in complex nonlinear tracking scenarios, the thermal infrared tracking problem is modeled as an ill-posed nonlinear operator equation, and a robust tracking framework is constructed by minimizing a function in Hilbert space. Second, the subquadratic penalty term preserves the convexity of the optimization problem, encouraging many elements in the sparse solution to approach zero, thus stabilizing the optimization process and enhancing sparsity. Furthermore, to more precisely capture sparsity, this paper extends the typical source conditions using Bregman distance to accommodate sparsity regularization. Under specific invertibility conditions in a finite-dimensional subspace, the proposed method effectively improves the convergence rate of the regularized solution. Experimental results on four large-scale infrared target tracking benchmarks demonstrate that the proposed tracking model outperforms state-of-the-art tracking algorithms in overall performance.