The traditional compressed sensing method for improving resolution is realized in the frequency domain. This method is affected by noise, which limits the signal-to-noise ratio and resolution, resulting in poor inversion. To solve this problem, we improved the objective function that extends the frequency domain to the Gaussian frequency domain having denoising and smoothing characteristics. Moreover, the reconstruction of the sparse reflection coefficient is implemented by the mixed L1_L2 norm algorithm, which converts the L0 norm problem into an L1 norm problem. Additionally, a fast threshold iterative algorithm is introduced to speed up convergence and the conjugate gradient algorithm is used to achieve debiasing for eliminating the threshold constraint and amplitude error. The model test indicates that the proposed method is superior to the conventional OMP and BPDN methods. It not only has better denoising and smoothing effects but also improves the recognition accuracy of thin interbeds. The actual data application also shows that the new method can effectively expand the seismic frequency band and improve seismic data resolution, so the method is conducive to the identification of thin interbeds for beach-bar sand reservoirs.