The present disclosure relates to a method and apparatus for processing of multi-dimensional readback signal from magnetic recording or optical, physical data recording so as to reduce/control Inter Symbol Interference (ISI) and noise within acceptable limits. The method is based on Partial Response Maximum Likelihood (PRML) detection and takes care of time varying channel conditions. In an embodiment, the filter coefficients of both the equalizer and the partial response (PR) target are jointly adapted to account for the channel condition for both separable and non-separable targets thus reducing signal detection complexity. In an aspect, the disclosure provides an apparatus that incorporates an adaptation engine along with the equalizer and the PR target that updates filter coefficients of both the equalizer and the PR target following the formulated mathematical equations.