In the present work, we address wavelet analysis, and the building blocks are shifts and dilates of a finite number of functions, namely wavelets. However, the construction of wavelet bases with convenient inner properties yields certain limitations. We circumvent these restrictions with the concept of wavelet frames, which allows for redundancy and provides more flexibility for the construction. In particular, we derive a family of arbitrarily smooth wavelet bi-frames in arbitrary dimensions with only two wavelets satisfying a variety of optimality conditions. Next, we determine the associated approximation rate of best N-term approximation, and finally, we apply our findings to image denoising.
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