Assessment of the Wavelet Transform for Noise Reduction in Simulated PET Images

An efficient method of tomographic imaging in nuclear medicine is positron emission tomography (PET). Compared to SPECT, PET has the advantages of higher levels of sensitivity, spatial resolution and more accurate quantification. However, high noise levels in the image limit its diagnostic utility. Noise removal in nuclear medicine is traditionally based on Fourier decomposition of images. This method is based on frequency components, irrespective of the spatial location of the noise or signal. The wavelet transform presents a solution by providing information on the frequency content while retaining spatial information. This alleviates the shortcoming of the Fourier transform and thus, wavelet transform has been extensively used for noise reduction, edge detection and compression. In this research, we used the SimSET software to simulate PET images of the NCAT phantom. The images were acquired using 250 million counts in a 128×128 matrix. For the reference image, we acquired an image with high counts (6 billion). Then, we reconstructed these images using our own software developed in MATLAB. After image reconstruction, a 250 million counts image (noisy image) and a reference image were normalized and then root-mean-square error (RMSE) was used to compare the images. Next, we wrote and applied de-noising programs. These programs were based on using 54 different wavelets and 4 methods. De-noised images were compared with the reference image using RMSE. Our results indicate that the Stationary Wavelet Transform and Global Thresholding are more efficient at noise reduction compared to the other methods that we investigated. The wavelet transform is a useful method for de-noising of simulated PET images. Noise reduction using this transform and loss of high-frequency information are simultaneous with each other. It seems that we should attend to the mutual agreement between noise reduction and the visual quality of the image.