Coarse quantization with the fast digital shearlet transform

Bernhard G. Bodmann; Gitta Kutyniok; Xiaosheng Zhuang

doi:10.1117/12.892720

27 September 2011 Coarse quantization with the fast digital shearlet transform

Bernhard G. Bodmann, Gitta Kutyniok, Xiaosheng Zhuang

Proceedings Volume 8138, Wavelets and Sparsity XIV; 81380Z (2011) https://doi.org/10.1117/12.892720
Event: SPIE Optical Engineering + Applications, 2011, San Diego, California, United States

Abstract

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.

Citation Download Citation

Bernhard G. Bodmann, Gitta Kutyniok, and Xiaosheng Zhuang "Coarse quantization with the fast digital shearlet transform", Proc. SPIE 8138, Wavelets and Sparsity XIV, 81380Z (27 September 2011); https://doi.org/10.1117/12.892720

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