Empirical Wavelet Frames

Due to their adaptive nature, empirical wavelets (EWs) had several successes in many fields from engineering, science, medical signal/image processing. Recently, a general theoretical framework has been developed in the one-dimensional case, showing the possibility to build EWs from any classic mother wavelets. Given extensive literature both in theory and applications of classic wavelet frames, it is legitimate to ask about the feasibility of building EW frames. We address this question in this paper. We prove several results which provide conditions on the existence of EW frames taking into account the above-mentioned adaptability.