A Combined Noise Reduction and Partial Volume Estimation Method for Image Quantitation

The partial volume effect is a corrupting artifact that affects nuclear imaging data such as PET and SPECT data and manifests as a blurring action on the resultant image data. This artifact is a result of the image acquisition process, where voxels in the PET or SPECT images are typically composed of a mixture of activity concentrations. This prevents accurate localization and quantitation of the target region activity. A further well-known image artifact found in most types of signal and image data is additive noise which is caused by limited photon count statistics for PET or SPECT imaging data. This work presents a novel methodology for statistically combining image noise reduction and partial volume estimation with particular application to low contrast to noise ratio image data. Each possible partial volume mixture is modeled as a Gaussian distribution and neighborhood statistical information is also incorporated in the form of the voxel neighborhood intensity mean, which has previously been shown to also be Gaussian distributed. This leads to an analytical solution of the optimal expected mean (thus minimizing the mean square loss), providing an equation that can iteratively and adaptively reduce the noise in each image voxel. Once the noise is reduced a further step that estimates the partial volume mixtures using an adaptive Markov Chain Monte Carlo method is found to improve the partial volume estimates in comparison to existing partial volume estimation techniques without a noise reduction step.