2011
DOI: 10.1109/tsp.2011.2144590
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Centralized and Distributed Semiparametric Compression of Piecewise Smooth Functions

Abstract: This thesis introduces novel wavelet-based semi-parametric centralized and distributed compression methods for a class of piecewise smooth functions. Our proposed compression schemes are based on a non-conventional transform coding structure with simple independent encoders and a complex joint decoder.Current centralized state-of-the-art compression schemes are based on the conventional structure where an encoder is relatively complex and nonlinear. In addition, the setting usually allows the encoder to observ… Show more

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Cited by 6 publications
(4 citation statements)
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“…Functions satisfying Strang-Fix conditions are extensively used in wavelet theory and the above result provides an intriguing connection between sampling of FRI signals and wavelets. This connection allows to combine FRI theory with wavelets to develop efficient centralized and distributed algorithms for the compression of piecewise smooth functions [38,39]. Finally, it is possible to show that any device whose input and output are related by linear differential equations can be turned into an exponential reproducing kernel and can therefore be used to sample FRI signals [9].…”
Section: 33mentioning
confidence: 99%
See 1 more Smart Citation
“…Functions satisfying Strang-Fix conditions are extensively used in wavelet theory and the above result provides an intriguing connection between sampling of FRI signals and wavelets. This connection allows to combine FRI theory with wavelets to develop efficient centralized and distributed algorithms for the compression of piecewise smooth functions [38,39]. Finally, it is possible to show that any device whose input and output are related by linear differential equations can be turned into an exponential reproducing kernel and can therefore be used to sample FRI signals [9].…”
Section: 33mentioning
confidence: 99%
“…By modeling the quantization error and any model mismatch as additive noise, one can use the CRB to estimate the performance of this compression strategy. The rate-distortion behavior of this FRI-based algorithm is [38,39]:…”
Section: Signal Compressionmentioning
confidence: 99%
“…Here, by PWS, we mean a signal that has a finite isolated set of discontinuities (jumps), and everywhere else the function has one or many continuous derivatives. The PWS noise removal problem has attracted considerable attention, in particular from those applying wavelet analysis in the signal and image processing communities (Chaisinthop and Dragotti, 2009;Mallat, 2009). For PWS signals, the level-set model is no longer parsimonious (but see the stack or threshold decomposition representation that is of central importance to morphological signal processing (Arce, 2005)).…”
Section: Piecewise Constant (Pwc) Versus Piecewise Smooth (Pws)?mentioning
confidence: 99%
“…4,15 FRI sampling theory has also had impact in specific applications such as image super-resolution, 2 for depth sensing, 13 for calcium transient detection 16 and in compression. 6,11 In this paper, we present a new framework for the sampling of FRI signals using arbitrary kernels and also present a local algorithm for the robust reconstruction of infinite streams of Diracs. The paper is organised as follows: in the next section we provide an overview of the theory of sampling signals with FRI, we present the local reconstruction algorithm in Sec.…”
Section: Introductionmentioning
confidence: 99%