In this work, we propose an overcomplete representation of multiview imagery for the purpose of compression. We present a rate-distortion (R-D) driven approach to decompose multiview datasets into two additive parts which can be interpreted as diffuse and specular content. We choose distinct and different sparsifying transforms for the diffuse and specular components and employ an R-D inspired measure as our optimization cost function to drive the decomposition based solely on compressibility. We first describe a framework which performs data separation in a registered domain to avoid the complexity of warping between views. Then a more comprehensive approach is proposed to separate specular data progressively from coordinates of multiple reference views. Experimental results show a coding gain of up to 0.6 dB for synthetic datasets and up to 0.9 dB for real datasets.