Partial volume and distribution estimation from multispectral images using continuous representations

Abstract

When estimating partial volume effects in the presence of noise, using neighboring information improves the estimation. The optimal linear transformation (OLT) is an unbiased minimum variance estimator. However, it does not use neighboring information and thus is sensitive to noise. We employ polynomial and B-spline continuous representations of the data to mathematically incorporate the neighboring information into the OLT. To evaluate the method, we use synthetic and actual images generated by simulation and acquired from phantoms and the human brain. Standard deviations of new estimators are up to 60% less than that of the OLT when the signal-to-noise ratio (SNR) is 25. As the SNR decreases, the proposed method demonstrates more improvements. Overall, B-spline estimators provide larger estimations of the standard deviation compared to polynomials. However, B-spline estimators outperform polynomials, providing an arbitrary degree of continuity. B-spline estimators are up to 10 times faster than polynomials and about 10 times slower than the OLT.