Wavelet-based denoising and its impact on analytical SPECT reconstruction with nonuniform attenuation compensation

In single photon emission computed tomography (SPECT), the nonstationary Poisson noise in projection data (sinogram) is a major cause of compromising the quality of reconstructed images. To improve the quality, we must suppress the Poisson noise in the sinogram before or during image reconstruction. However, the conventional space or frequency domain denoising methods will likely remove some information that is very important for accurate image reconstruction, especially for analytical SPECT reconstruction with compensation for nonuniform attenuation. As a time-frequency analysis tool, wavelet transform has been widely used in the signal and image processing fields and demonstrated its powerful functions in the application of denoising. In this article, we studied the denoising abilities of wavelet-based denoising method and the impact of the denoising on analytical SPECT reconstruction with nonuniform attenuation. Six popular wavelet-based denoising methods were tested. The reconstruction results showed that the Revised BivaShrink method with complex wavelet is better than others in analytical SPECT reconstruction with nonuniform attenuation compensation. Meanwhile, we found that the effect of the Anscombe transform for denoising is not significant on the wavelet-based denoising methods, and the wavelet-based de-noise methods can obtain good denoising result even if we do not use Anscombe transform. The wavelet-based denoising methods are the good choice for analytical SPECT reconstruction with compensation for nonuniform attenuation.