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Bit-patterned media (BPM) storage can have ultrahigh capacity, whereas the readback signal for the BPM storage is deteriorated by intersymbol interference in both the along- and across-track directions. As a detection method considering the two-dimensional (2D) interference, we propose a new structure of 2D partial response maximum likelihood (PRML) method based on a 2D partial response (PR) target and a 2D soft output Viterbi algorithm (SOVA) composed of two one-dimensional SOVAs. For the purpose of improving the bit error rate (BER) performance and reducing the computational complexity, the proposed method applies a 2D equalizer estimating the binary data recorded on the BPM instead of the output data of the 2D PR target. For this reason, the 2D PRML is located behind the 2D equalizer. Consequently, the proposed method has a superior BER performance as well as a low computational complexity. In addition, we carry out comparison of the BER performance in the 2D PRML according to the use of the least mean square and recursive least square algorithms in the 2D equalizer.