Multimodal Neuroimaging Fusion in Nonsubsampled Shearlet Domain Using Location-Scale Distribution by Maximizing the High Frequency Subband Energy

A fusion of medical imaging data obtained from different modalities plays an important role in the current clinical practice. In this paper, we propose a novel multimodal fusion algorithm for brain imaging data based on the statistical properties of nonsubsampled shearlet transform (NSST) coefficients and a novel energy maximization fusion rule. The marginal distributions of the high-frequency NSST coefficients exhibit heavier tails than the Gaussian distribution. As a consequence, after studying its characteristics, we use a heavy-tailed probability density function, student's t location-scale distribution, to describe the highly non-Gaussian statistics of empirical NSST coefficients by learning the parameters using maximum likelihood estimation. Then, we employ this model to develop a maximum a posteriori estimator to obtain the noise-free coefficients. Then, for the first time, a novel fusion rule for obtaining the fused NSST coefficients based on maximizing the energy in the high-frequency subbands is proposed. Experiments are carried out on fusing two or more multimodal neuroimages taken from the BrainWeb, Alzheimer's Disease Neuroimaging Initiative (ADNI), and Whole Brain Atlas databases. It is seen from the subjective and objective results that the proposed multimodal neuroimaging fusion method significantly outperforms the state-of-the-art methods including under noisy scenarios, and hence, it is more robust. It is also observed that the signal intensities in the fused images are better enhanced when a more number of source images are being fused. The proposed technique should benefit the medical professionals in diagnosing neurological disorders, such as Alzheimer, epilepsy, and multiple sclerosis.