Image-based correction for mismatched attenuation in PET images

Attenuation correction is essential for quantification in PET. The attenuation estimate is normally based on an additional measurement, e.g. transmission scan or CT, or on some calculation. If the estimate is inaccurate, the resulting emission images will show artefacts. For instance, a common problem is patient movement between the PET and CT scan. Using approximations we show that the error in the emission image is essentially local to where the attenuation mismatch occurred. We derive formulas for the error in the emission image and show that it is proportional to the error in the attenuation image. We present an approximate method to correct the emission image if it was computed with the wrong attenuation estimate. The method only needs the current emission image and an estimate for the attenuation mismatch, i.e. no further reconstruction is necessary. Moreover the correction term can be computed very fast. We show results with FBP and OSEM reconstructed images.