A manual measurement of blood vessels diameter is a conventional component of routine visual assessment of microcirculation, say, during optical capillaroscopy. However, many modern optical methods for blood flow measurements demand the reliable procedure for a fully automated detection of vessels and estimation of their diameter that is a challenging task. Specifically, if one measure the velocity of red blood cells by means of laser speckle imaging, then visual measurements become impossible, while the velocity-based estimation has their own limitations. One of promising approaches is based on fast switching of illumination type, but it drastically reduces the observation time, and hence, the achievable quality of images. In the present work we address this problem proposing an alternative method for the processing of noisy images of vascular structure, which extracts the mask denoting locations of vessels, based on the application of the continuous wavelet transform with the Morlet wavelet having small central frequencies. Such a method combines a reasonable accuracy with the possibility of fast direct implementation to images. Discussing the latter, we describe in details a new MATLAB program code realization for the CWT with the Morlet wavelet, which does not use loops completely replaced with element-by-element operations that drastically reduces the computation time.