Directional DCT And Directional DWT And Their Application In Ultrasound Images

Conventional 2-D discrete cosine transform (DCT) and 2-D discrete wavelet transform (DWT) have used in image processing extensively. In fact, they are all implemented separately through two 1-D transforms, one is along vertical, the other is horizontal. Apparently, they don't take image orientation into account. So it becomes a hot issue that how to incorporate the image orientation into DCT and DWT. At the same time, with the development of the ultrasonic imaging, ultrasonic imaging technology has become an important means of medicine diagnosis. However, speckle noise is produced in the process of the ultrasonic imaging, and it degrades severely the quality of the images. This is also a hot issue that how to remove the speckle noise.Aiming at the sectorial ultrasonic image, the paper makes a profound research of the above two issues. At first, according to the emission wave's directional characteristic of the sectorial ultrasonic, we build the sectorial mathematic model. Then we consider that the emission wave is launched from the circular point, so we can build the mathematic relationship for the emission wave conveniently by the polar coordinates equation f(r,θ). When fixing r, f(r,θ) can be seen as a arc of the sector; when fixingθ, f(r,θ) can be seen as a ray of the sector.According to the sectorial mathematic model, we put forward directional DCT and directional DWT separately along the radial and the arc. The principle of them is mapping the pixel points on rays or arcs into the disperse dots on lines, then transformed for the dots. Either the transforms are along the rays or the arcs, we only consider one aspect of the image's direction characteristic, so we put forward the 2-D directional DCT and 2-D directional DWT. They are all implemented separately through two 1-D transforms, one along the rays, the other along the arcs. Then, we apply the algorithm we proposed for degrading the speckle noise of ultrasonic image, and give the experiment result .compared with the experiment result of traditional 2-D DCT and 2-D DWT. The result proves that the means we proposed is better.In addition, considering the deficiency of DCT and DWT themselves, namely DCT is hard to remove the interference of the wide-band frequency, and DWT is hard to remove the interference of the narrow-band frequency. Then we put forward the hybrid transform algorithm of directional DCT and directional DWT, and also use it for degrading the speckle noise of ultrasonic image, finally give the experiment result.