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In this paper the new two-dimensional (TD) adaptive filter algorithms are introduced. The presented algorithms are TD variable step-size (VSS) normalized least mean squares (TD-VSS-NLMS) and TD-VSS affine projection algorithms (TD-VSS-APA). In these algorithms, the step-size changes during the adaptation which leads to the low steady-state mean square error (MSE), and fast convergence speed. We demonstrate the good performance of the derived algorithms in TD system identification and adaptive noise cancellation in digital images for image restoration.