We propose a reconstruction algorithm called al-goRIM for super-resolution fluorescence microscopy, based on speckle illuminations and image variance matching. Super-resolution with a factor two or close can be achieved under realistic conditions in terms of number of images and signal to noise ratio. Here, our key result is an approximation of the statistical variance equation, leading to a drastic reduction of the computational complexity. Moreover, we demonstrate that the unmodulated out-of-focus light does not contribute to the data variance, and that the statistical component due to noise can be estimated and removed in an unsupervised way, which is a crucial contribution to the practical robustness of algoRIM.