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Trellis based detection with pattern dependent noise prediction (PDNP) has become standard practice in the HDD industry. In a typical single-track signal processing scheme, the received samples from the read head are first filtered by a linear equalizer with a 1D partial response (PR). The linear filter output flows into a trellis-based (e.g. BCJR) detector that employs a super-trellis based on the PR mask ISI channel and a 1D pattern dependent noise prediction (1D PDNP) algorithm. The effective channel model has a media noise term which models signal dependent noise due to, e.g., magnetic grains intersected by bit boundaries. The media noise can influence two or more bit readback values. The trellis detector sends soft estimates of the coded bits to a channel decoder, which outputs estimates of the user information bits. There are two problems with traditional PDNP. First, when the number of tracks Nt simultaneously processed is greater than one, e.g. in two-dimensional magnetic recording (TDMR), the number of trellis states can become impractically large; this is the state explosion problem. Second, the relatively simple autoregressive noise model and linear prediction used in PDNP is somewhat restrictive and may not accurately represent the media noise, especially at high storage densities; this is the modeling problem. To address the state explosion problem, we separate the ISI detection and media noise prediction into two separate detectors and use the turbo-principle to exchange information between them, thus avoiding use of a super-trellis. To address the modeling problem, we design and train deep neural network (DNN) based media noise predictors. As DNN models are much more general than autoregressive models, they give a more accurate model of magnetic media noise than PDNP; this more accurate modeling results in reduced detector BERs compared to PDNP.