Two-dimensional (TD) adaptive filtering is a technique that can be applied to many image, and signal processing applications. This paper extends the one-dimensional adaptive filter algorithms to TD structures and the novel TD adaptive filters are established. Based on this extension, the TD variable step-size normalized least mean squares (TD-VSS-NLMS), the TD-VSS affine projection algorithms (TD-VSS-APA), the TD set-membership NLMS (TD-SM-NLMS), the TD-SM-APA, the TD selective partial update NLMS (TD-SPU-NLMS), and the TD-SPU-APA are presented. In TD-VSS adaptive filters, the step-size changes during the adaptation which leads to improve the performance of the algorithms. In TD-SM adaptive filter algorithms, the filter coefficients are not updated at each iteration. Therefore, the computational complexity is reduced. In TD-SPU adaptive algorithms, the filter coefficients are partially updated which reduce the computational complexity. We demonstrate the good performance of the proposed algorithms thorough several simulation results in TD adaptive noise cancellation (TD-ANC) for image restoration. The results are compared with the classical TD adaptive filters such as TD-LMS, TD-NLMS, and TD-APA

Keywords: Two Dimensional , Adaptive Filter , Noise Cancellation , Selective Partial Update , Variable Step-Size , Set-Membershi

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