We introduce iterative noise whitening for belief-propagation-based channel detectors over intersymbol interference channels with correlated additive noise. In particular, we consider longitudinal magnetic recording systems. The proposed "noise predictive belief propagation" (NPBP) detector iteratively whitens the noise samples by modifying the edge probability computation. NPBP detectors based on finite impulse response and infinite impulse response prediction filters are developed. In addition, we introduce a novel prediction filter optimization method leading to a better noise whitening performance. Simulation results for both coded and uncoded systems show that significant improvements can be obtained.