A new wavelet-based L ∞-constrained fixed and embedded coding technique is proposed in this paper. The embedded bit-stream can be truncated for any desired distortion bound at a corresponding bit-rate so that the target upper bound on the elements of the reconstruction error signal is guaranteed. The original image can also be coded up to a fixed a priori user-defined distortion bound, ranging up to lossless coding. A lifting-based wavelet decorrelating transform is employed on the original image and exact relations are established between spatial and wavelet domain distortions. The wavelet coefficients are quantized by symmetric uniform quantizers for fixed-distortion coding and by families of embedded uniform deadzone scalar quantizers for embedded coding. The quantized coefficients are finally losslessly encoded using a quadtree-based coding algorithm. Any floating-point lifting-based wavelet transform can be used, and a few of the popular wavelet transforms included in the JPEG2000 verification model are worked out as examples. We compare with other L ∞-constrained coding schemes and show that our proposed coder offers in addition a fully embedded L ∞oriented bit-stream. We illustrate also that the proposed coder retains the same capabilities as the state-of-the-art embedded wavelet-based codecs, while providing superior compression results and embeddedness with respect to the L ∞ distortion measure.

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Among the different classes of coding techniques proposed in literature, predictive schemes have proven their outstanding performance in near-lossless compression. However, these schemes are incapable of providing embedded L(infinity)-oriented compression, or, at most, provide a very limited number of potential L(infinity) bit-stream truncation points. We propose a new multidimensional wavelet-based L(infinity)-constrained scalable coding framework that generates a fully embedded L(infinity)-oriented bit stream and that retains the coding performance and all the scalability options of state-of-the-art L2-oriented wavelet codecs. Moreover, our codec instantiation of the proposed framework clearly outperforms JPEG2000 in L(infinity) coding sense.

In wavelet-based -constrained embedded coding, the bit-stream is truncated at the bit-rate that corresponds to a guaranteed, user-defined distortion bound. The letter analyzes the optimality of embedded deadzone scalar-quantizers for high-rate -constrained scalable wavelet-based image coding. A rate-distortion model applicable to the family of embedded deadzone scalar-quantizers is derived and experimentally validated. Conclusions are drawn regarding the optimal subband-quantizer instantiations. The optimal quantizers are employed in a coding algorithm that retains the coding performance and the flexibility options of wavelet-based codecs while allowing for a fully embedded -oriented bit-stream.Index Terms-Embedded scalar-quantizers, L-infinite norm, wavelet.

MESHGRID is a novel, compact, multi-scalable and animation-friendly 3D object representation method, which is part of MPEG-4, and which resides in the Animation Framework Extensions (AFX) toolset. The paper introduces the novel concept of local error control for arbitrary mesh encoding. In this sense, the paper proposes a new wavelet-based L ∞ -constrained coding technique for MESHGRID models, generating a fully scalable L ∞ -oriented bit-stream. The advantages of scalable L ∞ -oriented coding over 2 L coding are experimentally demonstrated.

We perform a statistical analysis of curvelet coefficients, distinguishing between two classes of coefficients: those that contain a significant noise-free component, which we call the "signal of interest," and those that do not. By investigating the marginal statistics, we develop a prior model for curvelet coefficients. The analysis of the joint intra-and inter-band statistics enables us to develop an appropriate local spatial activity indicator for curvelets. Finally, based on our findings, we present a novel denoising method, inspired by a recent wavelet domain method called ProbShrink. The new method outperforms its wavelet-based counterpart and produces results that are close to those of state-of-the-art denoisers.

The paper investigates the novel concept of local-error control in mesh geometry encoding. In contrast to traditional mesh-coding systems that use the mean-square error as target distortion metric, this paper proposes a new L-infinite mesh-coding approach, for which the target distortion metric is the L-infinite distortion. In this context, a novel wavelet-based L-infinite-constrained coding approach for meshes is proposed, which ensures that the maximum error between the vertex positions in the original and decoded meshes is lower than a given upper bound. Furthermore, the proposed system achieves scalability in L-infinite sense, that is, any decoding of the input stream will correspond to a perfectly predictable L-infinite distortion upper bound. An instantiation of the proposed L-infinite-coding approach is demonstrated for MESHGRID, which is a scalable 3D object encoding system, part of MPEG-4 AFX. In this context, the advantages of scalable L-infinite coding over L-2-oriented coding are experimentally demonstrated. One concludes that the proposed L-infinite mesh-coding approach guarantees an upper bound on the local error in the decoded mesh, it enables a fast real-time implementation of the rate allocation, and it preserves all the scalability features and animation capabilities of the employed scalable mesh codec.

A new wavelet-based embedded image coding technique is proposed. For any desired L ∞-distortion bound, the bit stream can be truncated at a corresponding bit-rate, so that the target upper bound on the absolute values of the pixels of the reconstruction error image is guaranteed. The algorithm outperforms embedded 2 L-oriented wavelet coders in terms of maximum absolute error.