Conventional one-way wave-equation migration methods often suffer from phase errors, amplitude distortions, and low-amplitude artifacts in the presence of strong lateral velocity variations, complex structures, and noisy data. To address these problems, we propose a sparse-denoising-constrained least-squares one-way wave-equation migration method. A one-way propagation operator is first constructed in the space–frequency domain using matrix eigenvalue decomposition to improve the stability and phase accuracy of wavefield depth extrapolation in laterally heterogeneous media. Recursive primary wavefield modeling is then used to establish the forward relationship between the reflectivity model and surface primary reflection data, and the data-misfit gradient is computed through adjoint propagation. Furthermore, a curvelet-transform denoiser regularization term is introduced, so that the data-residual gradient and denoising-residual gradient jointly guide the reflectivity update. Numerical experiments on the Lens, Marmousi, and Overthrust models show that the proposed method produces clearer reflection interfaces, more continuous events, and more stable residual convergence than least-squares migration based on the generalized-screen propagation operator. Noisy-data tests further demonstrate that the proposed sparse denoising constraint improves peak signal-to-noise ratio (SNR) and structural similarity index under 5 dB, 1 dB, and −5 dB noise conditions, especially preserving structural similarity under strong noise. These results demonstrate the improved stability, resolution, and structural fidelity of the proposed method for complex synthetic models and low-SNR synthetic data.