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If $K\\subset\\mathbb{R}^d$ is $k$-tiling $L^2(K)$ will admit a Riesz basis of exponentials. We use this result to construct generalized Riesz wavelet bases of $L^2(\\mathbb{R}^2)$, arising from the action of suitable subsets of the affine group. 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If $K\\subset\\mathbb{R}^d$ is $k$-tiling $L^2(K)$ will admit a Riesz basis of exponentials. We use this result to construct generalized Riesz wavelet bases of $L^2(\\mathbb{R}^2)$, arising from the action of suitable subsets of the affine group. 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