This paper proposes a spectral factorization of 2D responses based on the theory of partial minimum phase. It also presents a new decision feedback equalizer (DFE) based detector to be used optimally with minimum phase or partial minimum phase targets. This DFE structure can also be considered as an equalization scheme towards full and partial minimum phase targets. This paper also proves that if the channel is separable the partial minimum phase leads to a faster and less complex equalization that is advantageous for tracking the variation of the channel. These techniques are applied to 2D data storage on optical disks.