Monitoring aircraft using synthetic aperture radar (SAR) images is a very important task. Given its coherent imaging characteristics, there is a large amount of speckle interference in the image. This phenomenon leads to the scattering information of aircraft targets being masked in SAR images, which is easily confused with background scattering points. Therefore, automatic detection of aircraft targets in SAR images remains a challenging task. For this task, this paper proposes a framework for speckle reduction preprocessing of SAR images, followed by the use of an improved deep learning method to detect aircraft in SAR images. Firstly, to improve the problem of introducing artifacts or excessive smoothing in speckle reduction using total variation (TV) methods, this paper proposes a new nonconvex total variation (NTV) method. This method aims to ensure the effectiveness of speckle reduction while preserving the original scattering information as much as possible. Next, we present a framework for aircraft detection based on You Only Look Once v8 (YOLOv8) for SAR images. Therefore, the complete framework is called SAR-NTV-YOLOv8. Meanwhile, a high-resolution small target feature head is proposed to mitigate the impact of scale changes and loss of depth feature details on detection accuracy. Then, an efficient multi-scale attention module was proposed, aimed at effectively establishing short-term and long-term dependencies between feature grouping and multi-scale structures. In addition, the progressive feature pyramid network was chosen to avoid information loss or degradation in multi-level transmission during the bottom-up feature extraction process in Backbone. Sufficient comparative experiments, speckle reduction experiments, and ablation experiments are conducted on the SAR-Aircraft-1.0 and SADD datasets. The results have demonstrated the effectiveness of SAR-NTV-YOLOv8, which has the most advanced performance compared to other mainstream algorithms.