Suppression of background noise in clutter filtered contrast-free ultrasound microvasculature images is an important step towards better visualization, accurate segmentation, and subsequent morphological analysis of vascular structures. While different approaches to tackling this problem have been proposed, the use of denoising and vessel-enhancing filters has proven to be a straightforward and effective scheme. In this paper, we propose a multi-stage background noise removal framework, suited to microvasculature images, comprising sequential implementation of three different modes of suppressing noise and intensifying vascular patterns, namely self-similarity based collaborative filtering, mathematical morphology based denoising, and Hessian based vessel enhancement. We evaluate the effects of each filtering stage in the framework using in-vitro phantom data and compare the denoising performance of the framework with a number of existing noise removal approaches, as well as the clutter filtered images in the absence of noise suppression techniques, using in-vivo data from human subjects. The results indicate that the suggested method is, in many cases, capable of complete background noise removal, zeroing out most background regions, and improving signal-to-noise ratio and contrast-to-noise ratio in other regions by tens of dB compared to the other methods.