Structured illumination microscopy (SIM) can achieve a 2 × resolution enhancement beyond the classical diffraction limit by employing illumination translations with respect to the object. This method has also been successfully implemented in a "blind" configuration, i.e., with unknown illumination patterns, allowing for more relaxed constraints on the control of illumination delivery. Here, we present a similar approach using what we believe to be a novel super-resolution algorithm that employs a generalized version of the popular Richardson-Lucy algorithm, alongside an optimized and customized optical setup. Both numerical and experimental validations demonstrate that our technique exhibits high noise resilience. Moreover, by implementing random translations instead of "ordered" ones, noise-related artifacts are reduced. These advancements enable wide-field super-resolved imaging with significantly reduced optical complexity.