A study of wavelets combined, if desired, with other methods for use in edge sharpening of ultrasound images

Abstract

The increased use of laparoscopic surgery has resulted in a growing interest in use of ultrasounds. Ultrasounds do not have any known side effects, and it provides the surgeon with real-time imaging. In spite of its advantages, ultrasounds also have some disadvantages. The most obvious is that ultrasound images contain much noise. Another problem is that edges of vital organs may appear diffuse. In this thesis we will look at ways of sharpening edges by using a relatively new mathematical method called wavelet. With wavelets we analyse signals according to scale. This idea started with Fourier in the 1800’s, when he used sines and cosines to represent functions. After Fourier, mathematicians where led from frequency to scale analysis of functions. But it was not until the 1980’s that wavelets really came in to play. The work done by Ingrid Daubechies in 1990 was a milestone in the world of wavelets; she created a set of orthonormal basis functions. In this thesis our motive was to sharpen edges of blood vessels in ultrasound images. These edges may be both dark and diffuse, and our goal was to make them narrower and brighter. To find out if wavelets could be used for this purpose we developed a prototype application that implements the wavelet-based methods. With this application we performed some tests on very simple synthetic images containing edges. Our results imply that the Mexican hat wavelet is exceptionally well suited for finding and sharpening edges. We were able to “attune” the Mexican hat to the edge so that the centre of the edge became many times brighter, at the same time as the noise in the image was reduced. We were able to both located the two sides of the edge so that it could be made narrower manually, in addition to make the edge slimmer by means of wavelet transformation.