This essay has been submitted by a student. This is not an example of the work written by our professional essay writers.
Use of PET has been increasing very rapidly with regard to resolution and sensitivity during the recent past and had even found its applications in the Neurology and Onology. Functional neuroimaging is one of the emerging areas where data regarding the neuronal activities are being investigated (eg: data provided by PET). To attain the PET data it is compulsory to know the source of signal. The greatest asset of PET is that it measures the particular radio traces injected into the blood streams before imaging, a close example to this is the measure of cerebral glucose utilization with the tracer [18F] 2Fluoro-2-Deoxy-D-glucose.
Noise allied with PET:
As PET follows Poisson distribution, its noise properties also get changed due to the number of continuous applied corrections. This process there by would add-on more complexity in each noise source induced in the resulting PET and that would cause even more complicatedness in removing the noise. Having an idea on the source of noise in the reconstruction, noise induced in the PET can now be easily removed by post-Processing manner.
As PET signals are non-stationary, it does not exhibit global and periodic behaviours. Denoising PET data cannot depend on the Fourier analysis characteristics. Wavelets allow joint resolutions in special as well as frequency domains. Differing resolutions can be obtained by changing the scale of wavelets and its most important functions are of finite duration.
These are of two types i.e. Continuous Wavelet Transform(CWT) and Discrete Wavelet Transform(DWT).
It converts one dimensional signal to several wavelet coefficients. In these types of wavelets, signal expansion in mother wavelet is utilized to have the basis functions and are linked to each other by scale and position. WT i/p signal, scaled and translated basis functions are correlated to each other.
Â In this the one dimensional DWT of an i/p signal has discrete set of coefficients and is mostly represented as iterated structure of cascading low-pass and high-pass filters. Every WT in common has some approximations (high scale, low frequency(L) components) and details(low scale, high frequency(H) components) of their kind as shown in Fig(1). Multi resolution analysis of DWT was provided by cascading of the two filters that are mentioned above. DWT of particular image yields certain multi-resolution representations with certain amount of content represented by the each wavelet coefficient. Decomposition of an image in one dimension is even achieved by the process of cascading.
Removal of Noise by means of Wavelets:
Matlab is the one that provides much better depiction of the decomposition of an image during DWT, and is applied to obtain the PET data. The main use of the wavelet in particular application is to denoise i.e. in this process of denoising the areas where noise is present will be smoothed and the remaining areas that are not affected are left out. Adding up the noise to that of the actual signal contributes to the noisy coefficients. As noisy coefficients are those which add to every coefficient, signal is added to certain high amplitude coefficients. Thereby, this could be one of the great advantage of removing the noise(by noise thresholding) very easily from that of the signal( concentrated in limited coefficients).
Imaging process in Phantom using different wavelet filter implementation:
In this process Derenzo phantom is filled with 1.4m Ci of F-FDG and was PET scanned for couple of hours in one particular frame and there by sonogram was reconstructed with FBP using different filters such as Hamm, Ramp(amplifies high frequencies), Shepp(roll
representation of Derenzo phantom dimensions.
off at high frequency). There after SNR and resolution analysis was performed by using the phantom data i.e. is reconstructed. The resulting Pre, Post-Processing's are shown in Fig(4) below using FBP with different filters.
wavelet filter ‘a trous' , which means ‘with holes' i.e. particular filter where the threshold pixels within an image are set to 0. The main use of this wavelet filter in image denoising is to eliminate the noise within the actual image by adjusting noise to zero. Now the filter is being applied to the image in wavelet space and thereby this should reconstructed onto image space with the help of inverse wavelet transform[IWT].
ÂµCT image that was fused with the ÂµPET scan is shown in fig(5) and this ÂµCT image helps in providing the anatomical data to metabolic data of ÂµPET. Tumors can also be easily located in this ÂµCT image. Signal to noise ratio(SNR) is the only way to have the comparisons b/w filtered ÂµPET image and non-filtered ÂµPET image.
The overall process in this was to find out how far the wavelet filtering has helped in the resolution of images that are occurred as a result of FBP, ultimately the improvement in filter. From this process it can also be inferred that even if there is an error in the data , analysis b/w the filters and images make the data convincing. This data convincing is actually due to the decrease in the SNR and thereby increase in resolution. Practically it is somehow difficult to view the dissimilarities b/w both pre (a) and post (b) filtering , but the actual noise removed(c) image can be easily observed as shown in the Fig(6).
The quality of the image can be improved by the use of wavelets, i.e. wavelet post reconstruction. Occurrence of noise source is more in PET with regard to that of the repeated corrections and reconstructions of an image, this can be minimized by choosing the accurate threshold value, but is difficult to do so. As wavelets were introduced in Image processing, it's applications were extensively used in biomedicines in major aspects such as denoising, reconstructing the images using the pre, post processing. Wavelets added up with the filters can be used to reduce the noise. Wavelets are not a panacea, can also be implemented in the MatLab.
 Jansen, Maarten, Geert Uytterhoeven and Adhemar Bultheel. “Image De-noising by Integer Wavelet Transforms and Generalized Cross Validation.” Katholieke Universiteit Leuven, Department of Computer Science. Report TW 264, August 1997.
 “Wavelets in Medical Image Processing: De-noising, Segmentation, andRegistration.”
 Sahiner, Berkman and Andrew E. Yagle. “Image Reconstruction from Projections under Wavelet Constraints.” IEEE Transactions On Signal Processing. Vol. 41, No. 12, December 1993.
 Sakellaropoulos, P L Costaridou and G Panayiotakis. “A Wavelet-based Spatially Adaptive Method for Mammographic Contrast Enhancement.” Physics in Medicine and Biology. Vol. 48, 2003. pp. 787-803.
 Taswell, Carl. “The What, How, and Why of Wavelet Shrinkage Denoising.” Computing in Science & Engineering. May/June 2000.
 Unser, Michael and Akram Aldroubi. “A Review of Wavelets in Biomedical Applications.” Proceedings of the IEEE. Vol. 84, No. 4, April, 1996.
 Unser, Michael and Thierry Blu. “Wavelet Theory Demystified.” IEEE Transactions On Signal Processing, Vol. 51, No. 2, February 2003.