Hadamard single-pixel imaging (HSI) is an appealing imaging technique due to its features of low hardware complexity and industrial cost. To improve imaging efficiency, many studies have focused on sorting Hadamard patterns to obtain reliable reconstructed images with very few samples. In this study, we present an efficient HSI imaging method that employs an exponential probability function to sample Hadamard spectra along a direction with better energy concentration for obtaining Hadamard patterns. We also propose an XY order to further optimize the pattern-selection method with extremely fast Hadamard order generation while retaining the original performance. We used the compressed sensing algorithm for image reconstruction. The simulation and experimental results show that these pattern-selection method reliably reconstructs objects and preserves the edge and details of images.