We present a novel method, to our knowledge, to synthesize non-trivial speckle patterns that can enable sub-Rayleigh second-order correlation imaging. The speckle patterns acquire a unique anti-correlation in the spatial intensity fluctuation by introducing the blue noise distribution on spatial Fourier power spectrum to the input light fields through amplitude modulation. Illuminating objects with the blue noise speckle patterns can lead to a sub-diffraction limit imaging system with a resolution more than three times higher than first-order imaging, which is comparable to the resolving power of ninth order correlation imaging with thermal light. Our method opens a new route towards non-trivial speckle pattern generation by tailoring amplitudes in spatial Fourier power spectrum of the input light fields and provides a versatile scheme for constructing sub-Rayleigh imaging and microscopy systems without invoking complicated higher-order correlations.