Locally adaptive image filtering for noise reduction in PET

As well known, the signal-to-noise ratio (SNR) of PET images can be low. This is especially true for whole body examinations of heavy patients, for respiratory-gated studies, and dynamic studies with short frames. In these cases linear smoothing filters (LF) such as a Gaussian filter are usually applied in order to achieve an acceptable SNR. Image resolution is, however, reduced by these LFs. This affects detectability and quantification of small structures. Interesting alternatives to LFs are non-linear, locally adaptive filters (NLF), which enable noise reduction while preserving strong edges in the data. It was the aim of this study to investigate the performance of a special NLF (bi-lateral filter, BF) when applied to low SNR images in PET.

Methodik/Methods:

The BF consists of the product of a spatially dependent part and an intensity dependent part. In one spatial dimension the filter weights are defined as W(n-n0) = S * exp(-(n-n0)2/2/sn2) * exp(-(I(n)-I(n0))2/2/sI2) where n0 is the index of the target voxel, n is the index of neighboring voxels, sn is the spatial standard deviation, I(n), I(n0) are the intensities of n and n0, sI is the intensity standard deviation, and S normalizes the sum over all weights to unity. Due to the intensity dependence this filter is not invariant but adjusted individually for each choice of n0, thus it is locally adaptive. The filter works by penalizing voxels, which are distant from n0 either in the spatial or the intensity domain. The latter property leads to preservation of sharp edges. To quantify the effects of this filter, phantom measurements were performed with F-18 using a cylinder phantom (∅=20 cm, h=18 cm; 6 spheres with 2.7 - 27 ml). Three different sphere-to-background ratios were investigated in list-mode in order to assess different SNR levels. The image data were filtered, both with the BF and a LF. The filtered data were analyzed for changes in noise level, resolution, and signal recovery. Furthermore, clinical respiratory-gated whole body studies were investigated with BF and compared to LF filtered images.

Ergebnisse/Results:

In the phantom studies the BF is able to preserve the spatial resolution of the original data near the edges of the spheres while improving the noise characteristics. Signal recovery even of small spheres is not significantly reduced. Using the LF seriously compromises spatial resolution and leads to unacceptable reduction of signal recovery. The positive properties of the filter were also apparent when applying the BF to single gates of respiratory-gated studies, which otherwise were not suitable for visual inspection.

Schlussfolgerungen/Conclusions:

NLF is a powerful alternative to LF, especially for studies with high noise. Its performance, however, critically depends on a sensible choice of the intensity standard deviation sI. Further work will show whether the filter is suitable for clinical use.