The classical restoration algorithm can not effectively recover the full frequency domain information of the object, which leads to the serious optical sidelobes. In this paper, the application of metal nano arrays in structured light illumination is studied, and the problem of optical sidelobes in plasmonic structured illumination microscopy is solved using Maximum A Posteriori (MAP) estimation. The research shows that the MAP estimation method can effectively restore the high spatial frequency information, and through the reasonable selection of optimization parameters to achieve the purpose of suppressing optical sidelobes. At the wavelength of 520 nm, 1.3 numerical aperture, the lateral resolution can be obtained at FWHM of 65 nm, which is about 3.6 times of the traditional fluorescence microscope. This technology has potential application application in the field of life science.