Noise Processing for Simple Laplacian Pyramid Synthesis Based on Dual Frame Reconstruction

1. Keep simple conventional reconstruction • Achieve gains offered by dual frame reconstruction • Since we process at the encoder itself. Single level decomposition Single level reconstruction Quantization • Proposed by Do and Vetterli in 2003 Analysis operator has multiple left-inverses • Optimal synthesis operator Conventional Reconstruction Dual Frame Reconstruction • Proposed structure implements if and only if • , i.e., biorthogonality • , i.e., is an orthogonal projector • Practically, the proposed structure offers gains even if above conditions are not strictly met, e.g., about 1 dB gain for the 9/7 filters. Noise Processing for Simple Laplacian Pyramid Synthesis Based on Dual Frame Reconstruction Aditya Mavlankar, David Chen, Sameh Zakhary, Markus Flierl and Bernd Girod Information Systems Laboratory, Stanford University, Stanford, CA 94305, USA Laplacian Pyramid: Background Encoder-Side Noise Processing Extension to Multiple Levels Conventional Reconstruction (b) Noise processing method A (a) Conventional encoder or equivalently, • Proposed by Burt and Adelson in 1983 • Laplacian pyramid (LP) is overcomplete • Key differences of LP from critically sampled filterbanks • Freedom in the design of filters • Multiple reconstruction methods • Reduced aliasing in highpass subbands Experimental Results Lena (512x512) Dual Frame Reconstruction (c) Noise processing method B Conclusions Einstein (512x512) • Reconstruction procedure proposed by Do and Vetterli achieves roughly 1 dB gain for 9/7 filters • Similar gain is achievable by our proposed encoder-side noise processing while retaining simple synthesis • The same simple decoder can be employed for both open-loop and closed-loop encoding; simple decoder is optimal for closed-loop encoding anyway • Overall complexity of encoder and decoder combined is the same as for dual frame reconstruction; roughly half of the complexity is shifted from the decoder to the encoder Contact {maditya, dmchen, zakhary, mflierl, bgirod} @ stanford.edu One decomposition level (left) and four decomposition levels (right)