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This brief proposes a new transform-domain (TD) regularized M-estimation (TD-R-ME) algorithm for a robust linear estimation in an impulsive noise environment and develops an efficient QR-decomposition-based algorithm for recursive implementation. By formulating the robust regularized linear estimation in transformed regression coefficients, the proposed TD-R-ME algorithm was found to offer better estimation accuracy than direct application of regularization techniques to estimate system coefficients when they are correlated. Furthermore, a QR-based algorithm and an effective adaptive method for selecting regularization parameters are developed for recursive implementation of the TD-R-ME algorithm. Simulation results show that the proposed TD regularized QR recursive least M-estimate (TD-R-QRRLM) algorithm offers improved performance over its least squares counterpart in an impulsive noise environment. Moreover, a TD smoothly clipped absolute deviation R-QRRLM was found to give a better steady-state excess mean square error than other QRRLM-related methods when regression coefficients are correlated.