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Thermal asperities (TAs) cause a crucial problem in magnetic recording systems because they can cause a burst of errors in data detection process. Without a TA detection and correction algorithm, the system performance can be unacceptable, depending on how severe the TA effect is. This paper proposes an iterative scheme to suppress the TA effect. This scheme jointly performs TA suppression and turbo equalization on the partial-response channels with error-correction codes. At each turbo iteration, an improved readback signal is obtained by subtracting the reconstructed TA signal from the TA-affected readback signal, where the reconstructed TA signal is computed based on a least-squares fitting technique with an aid of soft decisions from previous turbo iterations. Simulation results indicate that the proposed scheme outperforms the conventional receiver with separate TA suppression and turbo equalization, and is only marginally more complex than the conventional receiver.