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This paper presents a method to find the operational rate-distortion optimal solution for an overcomplete signal decomposition. The idea of using overcomplete dictionaries, or frames, is to get a sparse representation of the signal. Traditionally, suboptimal algorithms, such as matching pursuit (MP), are used for this purpose. When using frames in a lossy compression scheme, the major issue is to find the best possible rate-distortion (RD) tradeoff. Given the frame and the variable length code (VLC) table embedded in the entropy coder, the solution to the problem of establishing the best RD tradeoff is highly complex. The proposed approach reduces this complexity significantly by structuring the solution approach such that the dependent quantizer allocation problem reduces to an independent one. In addition, the use of a solution tree further reduces the complexity. It is important to note that this large reduction in complexity is achieved without sacrificing optimality. The optimal rate-distortion solution depends on the selection of the frame and the VLC table embedded in the entropy coder. Thus, frame design and VLC optimization is part of this work. We experimentally demonstrate that the new approach outperforms rate-distortion optimized (RDO) matching pursuit, previously proposed by Gharavi-Alkhansari.