We present a novel method for detecting circles on digital images. This transform is called the circlet transform and can be seen as an extension of classical 1D wavelets to 2D: each basic element is a circle convolved by a 1D oscillating function. In comparison with other circle-detector methods, mainly the Hough transform, the circlet transform takes into account the fi- nite frequency aspect of the data: a circular shape is not restricted to a circle but has a certain width. The transform operates directly on image gradient and does not need further binary segmentation. The implementation is effi- cient as it consists of a few Fast Fourier Transforms. The circlet transform is coupled with a soft-thresholding process and applied to a series of real images from different fields: ophthalmology, astronomy and oceanography. The results show the effectiveness of the method to deal with real images with blurry edges.