The frequency-difference (FD) method uses the FD Hadamard product, comprising auto-products to model below-band acoustic fields and unintended cross-products, for efficient direction-of-arrival (DOA) estimation under spatial aliasing. Despite improved resolution from compressive sensing, spurious peaks arise as a result of cross-products lacking counterparts in the sensing matrix. The proposed method addresses this by reconstructing the sensing matrix with the full Hadamard product and applying sparse Bayesian learning to estimate a two-dimensional hyperparameter matrix, extracting its diagonal to suppress spurious DOAs. Simulations show that it outperforms previous compressive FD methods in detecting weak targets, where advantages increase as source numbers grow.