This paper proposes a method for learning background restoration for infrared small target detection, employing a lo- cal sparse dictionary alongside an equalized structural texture representation. The method is specifically designed for the detection of small infrared targets, accommodating various levels of brightness, spatial size, and intensity. Our proposed model intelligently combines global low-rankness and local sparsity to estimate the rank of the background tensor, leveraging spatial and structural information to overcome the limitations posed by insufficient detailed texture knowledge. Subsequently, a structural texture representation, combining local gradient maps and local intensity maps, is applied to emphasize small objects. By comparing our method with nine advanced and representative approaches and quantifying the comparison using various metrics, the experimental results indicate that our proposed method has achieved favorable outcomes in both quantitative assessments and visual results.