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Radio frequency transceivers operating in in-band full-duplex or frequency-division duplex mode experience strong transmitter leakage. Combined with receiver nonlinearities, this causes intermodulation products in the baseband, possibly with higher power than the desired receive signal. In order to restore the receiver signal-to-noise ratio in such scenarios, we propose two novel digital self-interference cancellation approaches based on spline interpolation. Both employ a Wiener structure, thereby matching the baseband model of the intermodulation effect. Unlike most state-of-the-art spline-based adaptive learning schemes, the proposed concept allows for complex-valued in- and out-put signals. The optimization of the model parameters is based on the stochastic gradient descent concept, where the convergence is supported by an appropriate step-size normalization. Additionally, we provide a gain control scheme and enable pipelining in order to facilitate a hardware implementation. An optional input transform improves the performance consistency for correlated sequences. In a realistic interference scenario, the proposed algorithms clearly outperform a state-of-the-art least mean squares variant with comparable complexity, which is specifically tailored to second-order intermodulation distortions. The high flexibility of the spline interpolation allows the spline-based Wiener models to match the performance of the kernel recursive least squares algorithm at less than 0.6% of the arithmetic operations.