Non-iterative correction for collimator blurring

Abstract

1752

Objectives: In SPECT, collimators cause distance-dependent blurring in projections and in reconstructed images. Iterative reconstruction algorithms are the state-of-the-art methods to compensate for this effect, but they are slow. The Frequency-Distance Principle (FDP) can also be used to compensate for this effect. The FDP method is a non-iterative, pre-processing, approximate method; it ignores the attenuation effect and gives a poor approximation for low-frequency components. We propose an efficient, post-processing, non-iterative method to compensate for this effect. Methods: The proposed method consists of 3 steps. First, use an efficient (analytical or iterative) naive image reconstruction algorithm to reconstruct a raw image with attenuation correction. Since the reconstruction algorithm does not correct for the spatially variant point spread function (PSF), the reconstructed raw image has a spatially variant PSF. Second, we further blur the raw image using a spatially variant kernel to obtain a blurrier image which has a spatially INVARIANT PSF. Third, an efficient, shift-invariant filtering method is used to deblur the blurrier image. If the camera rotates in a circular orbit, the spatially variant PSF in the raw image is radially isotropic. The PSF at the center of rotation has circular contours. The PSF at the off-center positions has elliptical contours and the major axis of the ellipses is in the radial direction. Thus the 2nd step, i.e., the further blurring step, can be achieved by the following rotational convolution method. The raw image is rotated about the center of camera rotation for small incremental angles, clockwise and counterclockwise. A weighted sum of the rotated versions (including the un-rotated version) is formed. The weighting factots vary with the distance to the center of rotation. The summed image has a shift invariant PSF, and is easy to deblur by any shift-invariant filtering method. Results: In a simulation, a regular FBP algorithm was used in the 1st step. The incremental rotation angle in the 2nd step was 1°. The rotation range was (-5°, 5°). A Fourier domain deblurring method is used in the 3rd step. Conclusions: A non-iterative method is proposed to compensate for non-stationary PSF in an image. This method first further blurs the image with a non-stationary kernel, to obtain a blurrier image with a stationary PSF, which can be deblurred efficiently.