Image reconstruction without the Gibbs artifacts

Objectives The state-of-the-art image reconstruction algorithms in nuclear medicine are the iterative algorithms (e.g. ML-EM and OS-EM). The iterative methods are able to model the data noise, attenuation, and the point spread function (PSF). When the PSF is modeled, the Gibbs ringing artifacts usually show up in the reconstruction. These artifacts are severe at the edges of large image intensity jumps. The goal of the proposed method is to develop a post-processing technique to compensate for the PSF without introducing the Gibbs artifacts.

Methods Our method first uses an iterative algorithm (e.g., ML-EM or OS-EM) to reconstruct the image with attenuation correction. The PSF compensation is not performed at this stage. We refer to this reconstruction as the raw reconstruction. We then use a novel split Wiener filter to compensate for the PSF and control the noise. The 1D convolution kernel of a Wiener filter is symmetric. We split the kernel in half, obtaining the left-half and the right-half kernels. Two filtered images are obtained with these two kernels. One image has the Gibbs ringing on one side of the jumps, while the other image has the ringing on the other side. A selective combination technique is then used to combine these two images. This post-processing method is applied to the raw reconstruction one dimension at a time. We realize that the Wiener filter can only compensate for a stationary PSF. We apply a further blurring procedure, which converts the non-stationary PSF into a stationary PSF, to the raw reconstruction before the split Wiener filtering is applied.

Results Computer simulations are conducted to compare the OS-EM reconstruction that compensates for the PSFwith the proposed split Wiener filtering method. The phantom is a uniform square using both noiseless and noisy data. The OS-EM method gives severe Gibbs artifacts, but the proposed method does not.

Conclusions We have developed an image reconstruction algorithm that is able to compensate for attenuation and non-stationary PSF. This newly developed algorithm is Gibbs artifact free and is much faster than iterative algorithms that compensate for the PSF during reconstruction