In this paper, we propose a novel method for 2D pattern recognition by extracting features with the log-polar transform, the dual-tree complex wavelet transform (DTCWT), and the 2D fast Fourier transform (FFT2). Our new method is invariant to translation, rotation, and scaling of the input 2D pattern images in a multiresolution way, which is very important for invariant pattern recognition. We know that very low-resolution sub-bands lose important features in the pattern images, and very high-resolution sub-bands contain significant amounts of noise. Therefore, intermediate-resolution sub-bands are good for invariant pattern recognition. Experiments on one printed Chinese character dataset and one 2D aircraft dataset show that our new method is better than two existing methods for a combination of rotation angles, scaling factors, and different noise levels in the input pattern images in most testing cases.