Image Reconstruction Algorithm Based On Wavelet Multiresolution Analysis

Computerized Tomography (CT) is a typical non-invasive examination techniques in medicine,which can depict anatomical structures without damaging the human body.lt is based on the principle: under a number of angles, the X-Ray attenuation in a cross section of a human body is measured by detector resulting in a set of profiles. This set of profiles is called the Radon Transfoim of the object in mathematics. The problem now is to reconstruct a two-dimensional image via inverting its Radon Transform. But In the process of the inverted Radon Transform, the recovery of an image at any fixed point requires the knowledge of all projections of the image. This means that a patient would have to be exposed to a relatively large amount of X-Rays even if it was desired to view only a small part of the patient's body. Thus, searching for a means to reduce exposure, and at the same time to be able to perfectly reconstruct the region of interest (ROI), so-called Local Tomography, has been of great interest recently.The wavelet transform theory is one of the effective tools mat widely apply to image processing recently, which have charicrictics of multiresolution analysis, fast working time, etc. So it is nature that conbine the wavelet theory with image reconstruction.In this paper, firstly, we studied the newly working in the field of the application of wavelets transform used- in the computer tomography in two-dimesion, and mainly focused in the field of filter-backprojection algorithm. We analized the application of one-demision wavelets transform and two-demision wavlets transform. We fould that most reconstruction algorithm based on wavelets did not consider about the noise. And so, we proposed the denoised reconstruction algorithm based on seperable MRA, in which added regularizion denoised method based on wavelets. This algorithm not only have the charicristic of local reconstruction that could reduce the amount of X-ray exposure and computations in reconstruction , but could reduce the noise in the conditions of keep same image quality as reconstructed in the filter-backprojection algorithm as well.And then, we proposed wavelets reconstruction algoritlim based on non-seperable MRA and wavelets donoise reconstruction algoritlun based on non-seperable MRA. In recent study, when people applied the two-demision waveletstransform in the reconstruction algorithm, they usually filtered the image by rows and columns in turn, that is supposed the image could be separated by variable x and y. But in the real world, the two demision signals could not be separated in most time. The two demision image should be considers as areas rather than as rows and columns, and thus can be better handled by a truly two dimensional transform.The wavelets reconstruction algorithm based on non-seperatable MRA filtered the projection data by two-demesions filter. This kind of two-channels wavelets decomposition methed reconstruct the wavelet coefficients of an image from the Radon transform data, and these coefficients were made reverted wavelet transform obtain the original image . Wavelets subsampled on the quincunx lattice, which can have cut-off at an angle during the wavelets decomposition. This is better psychovisually because it means that the perceptually least valuable component of vision is quantized first. Simulations were carried out with the Shepp-Logan brain phantom. The constructions do not only have the property of local reconstruction as same as the wavelet reconstruction algorithm based on separable MRA, but also had better image qulity and computions. Then we put the soft-thresolding denoising method based on wavelets in the algorithm. The coefficients used to synthesize the reconstruction after being denoised by the method. And so the method whichhas the same quality as filtered backprojection algorithm, used the properties of wavelet to reconstruct a local region of the cross section of a body, using almost completely local data, and could reduce noise of the image.