Coarse quantization with the fast digital shearlet transform
Bernhard G. Bodmann, Gitta Kutyniok, Xiaosheng Zhuang · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2011
The fast digital shearlet transform (FDST) was recently introduced as a means to analyze natural images efficiently, owing to the fact that those are typically governed by cartoon-like structures. In this paper, we introduce and discuss a first-order hybrid sigma-delta quantization algorithm for coarsely quantizing the shearlet coefficients generated by the FDST. Radial oversampling in the frequency domain together with our choice for the quantization helps suppress the reconstruction error in a similar way as first-order sigma-delta quantization for finite frames. We provide a theoretical bound for the reconstruction error and confirm numerically that the error is in accordance with this theoretical decay.