Dynamic Magnetic Resonance Imaging (DMRI) is an imaging technology that acquires images through continuous scanning to capture their changes over time and space. Applying compressed sensing technology to DMRI tends to result in unsatisfactory visual quality of the reconstructed magnetic resonance images. Therefore, to address the deficiencies of compressed sensing in DMRI reconstruction, a reconstruction model based on low-rank and sparse decomposition is proposed by using L1 norm to characterize the sparsity of magnetic resonance image data and utilizing low-rank to describe the intrinsic correlation of dynamic magnetic resonance image sequences. This effectively reduces artifacts in dynamic magnetic resonance imaging. In the modeling phase, the sparse component is modeled using the L1 norm, while the low-rank component is modeled using the nuclear norm. In the model optimization phase, a wavelet framework regularization method is introduced, and the reconstruction model is transformed into a non-smooth convex optimization problem, which is then solved by using a momentum-accelerated proximal gradient method. Finally, experiments are conducted on cardiac cine, cardiac perfusion, and phantom membrane image data to verify the effectiveness of the proposed model. The experimental results show that the average PSNR and the average SSIM of the proposed method reach 33.7090 dB and 0.9660 at a sampling ratio of 30%，respectively，which further improves the reconstruction accuracy of the dynamic magnetic resonance image.