Abstract: Multiplicative speckle noise is an inherent part of coherent imaging systems, such as synthetic aperture radar and digital holography. Speckle noise is mitigated by obtaining multiple measurement vectors with independent speckle noise, a technique commonly referred to as "multi-look", followed by appropriate averaging. However, in many applications, even with multi-look, the achievable performance is not satisfactory. Moreover, in this approach, every look (or every set of measurements) is required to be over-determined,which imposes additional constraints on spatial resolution. In this work, we develop a maximum likelihood based approach for recovering images from a set of compressive measurements contaminated by speckle noise. We propose an iterative multi-look compressive sensing recovery algorithm, DIP-$M^3$, that i) requires no training data, ii) is computationally efficient, and iii) generates high-quality reconstruction images from multi-look, where each look is underdetermined and corrupted by speckle noise.