1. A nano-scale resolution fluorescence microscopy system, comprising: a speckle pattern generator configured to generate speckle patterns by passing, through a diffuser, a light emitted from at least one coherent light source in at least one color to detect fluorescent emission in at least one color from fluorophores attached to a specimen; an illumination optical system to radiate the generated speckle patterns to be exposed on a specimen, by disposing at least one optical lens; and a fluorescent image optical system configured to detect fluorescence emission images of the specimen excited by the speckle patterns in at least one color, by passing the radiated speckle patterns sequentially through at least one excitation filter and detecting the emission images through at least one emission filter; and an image reconstruction algorithm configured to sequentially obtain fluorescent emission images by the fluorescent image optical system, and to reconstruct the image at high resolution by detecting temporal profile of fluorescence emission data at every pixel, based on the sequentially obtained images, wherein the image reconstruction algorithm is configured to process fluorescence emission images obtained sequentially based on any type of array signal processing algorithms that uses data covariance matrix by calculating the spatial correlation matrix between pixels, and reconstruct images with respect to the fluorophores using the signal and noise subspace structure of the data covariance matrix.