Infrared small target detection has recently benefftted greatly from deep neural models. However, existing frameworks generally ignore effective global information modeling, leading to poor detection when the target has high similarity to the background. We propose a dual-branch detection framework BFCD-Net, to address the above challenges through a clever combination of neural low-rank background modeling and multi-dimensional feature characterization. In neural low-rank background modeling. We adopt low-rank prior neural functions and neural regularization to effectively capture the global and local properties of the background. Specifically, the BFCD-Net framework contains a feature enhancement module, a distinguishing convolution kernel module, and a dynamic detector. The feature enhancement module improves network perception of targets by enlarging image resolution and enhancing the features of target. The distinguishing convolution kernel module enhances contrast between targets and backgrounds through adaptive feature segmentation and differential convolution operations. The dynamic detector optimizes feature representation and decision processes through adaptive weight learning. Additionally, we introduce an anti-wavelet transform fusion module to enhance multi-scale feature integration capabilities, and employs a three-dimensional total variation constraint to further improve the robustness of background modeling. Meanwhile, we propose a LGdicefunction. It improves the accuracy of the model in infrared small target detection tasks by explicitly focusing on the discrepancy between the predicted results and the real target. Experimental results demonstrate that BFCD-Net delivers superior detection performance across challenging datasets, especially on the NUDT-SIRST dataset, the IoU and Precision reach 84.55% and 94.99%. BFCD-Net provides an innovative solution for efficient and robust infrared small target detection.