Automatic target recognition in synthetic aperture radar (SAR) images is a challenging task due to the unique imaging mechanism of SAR images. To address the speckle noise and intensity variations caused by different SAR operating conditions, we propose a novel target recognition approach that is implemented via multi-scale perception (MSP) and denoising representation (DR). Specifically, we first design the MSP method for feature extraction which takes advantage of sparse random projections of multi-scale features. This sparsity allows us to avoid computational redundancy and obtain a more extensive local difference pattern than Haar-like features. We then construct the DR model for target identification which introduces noise components into the sparse representation model to isolate local intensity errors. Experiments on the moving and stationary target acquisition and recognition dataset are used to validate the performance of our proposed method. In the presence of significant noise corruption and depression angle variations, our method demonstrates superior performance compared to some representative methods, including traditional machine learning methods and convolutional neural network-based methods.