We propose a method for increasing the resolution of an aperture limited optical system by illuminating the input with a speckle pattern. The high resolution of the projected speckle pattern demodulates the high frequencies of the sample and permits its passage through the system aperture. A decoding provides the superresolved image. The speckle pattern can be generated in a simple manner in contrast with other structured light superresolution methods. The method is demonstrated in microscopy test images.