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This paper presents a novel digital domain self-interference (SI) cancellation scheme for full-duplex (FD) OFDM systems employing noise robust SI channel estimation technique. First using the least-square (LS) technique, both the desired and the SI channels are estimated jointly assuming that the desired as well as SI signals are perfectly known. Since, LS estimator does not consider any noise effect in obtaining its solution, it may suffers from noise. Next, to suppress the noise effect, we propose wavelet decomposition (WD) of SI channel estimate to perform denoising in time domain. In the proposed algorithm, a standard deviation of noise obtained by WD is used as a threshold value which is a requisite to achieve an optimal performance. The simulation results show that the proposed algorithm outperforms the joint LS algorithm as well as the previous works using conventional LS where the desired signal is assumed as noise.