This paper describes a novel video coding scheme based on a three-dimensional Matching Pursuit algorithm. In addition to good compression performance at low bit rate, the proposed coder allows for flexible spatial, temporal and rate scalability thanks to its progressive coding structure. The Matching Pursuit algorithm generates a sparse decomposition of a video sequence in a series of spatio-temporal atoms, taken from an overcomplete dictionary of three-dimensional basis functions. The dictionary is generated by shifting, scaling and rotating two different mother atoms in order to cover the whole frequency cube. An embedded stream is then produced from the series of atoms. They are first distributed into sets through the set-partitioned position map algorithm (SPPM) to form the index-map, inspired from bit plane encoding. Scalar quantization is then applied to the coefficients which are finally arithmetic coded. A complete MP3D codec has been implemented, and performances are shown to favorably compare to other scalable coders like MPEG-4 FGS and SPIHT-3D. In addition, the MP3D streams offer an incomparable flexibility for multiresolution streaming or adaptive decoding.

Uniform scalar quantizers are widely used in image coding. They are known to be optimum entropy constrained scalar quantizers within the high resolution assumption. In this paper, we focus on the design of nearly uniform scalar quantizers for high performance coding of wavelet coefiqcients whatever the bitrate is. Some codecs use uniform scalar quantizers with a zero quantization bin size (deadzone) equal to two times the other quantization bin sizes (for example JPEG2000). We address the problem of deadzone size optimization using distortion rate considerations. The advantages of the proposed method are that the quantizer design is adapted to both the source statistics and the compression ratio. Our method is based on statistical information of the wavelet coefiqcients distribution. It provides experimental gains up to 0.19 dB.

by Rebecka Jenny Jornsten Doctor of Philosophy in Statistics University of California, Berkeley Professor Bin Yu, Chair This thesis consists of three parts. Even though each part is self-contained, a common theme runs through all of them: data compression and its implications for statistical inference. In particular, we consider the following three questions. How can we quantify the effect of compression on statistical inference? How should a compression scheme be designed such that the effect of compression on inference is minimal? How can the Minimum Description Length (MDL) principle be used for model selection with an extraordinary number of dependent predictors? In this thesis, we attempt to answer these three questions in a general setting, and with a specific application in the compression and analysis of microarray images.

Our goal in this paper is to provide a fast numerical implementation of the local trigonometric bases algorithm1 in order to demonstrate that an advantage can be gained by constructing a biorthogonal basis adapted to a target image. Different choices for the bells are proposed, and an extensive evaluation of the algorithm was performed on synthetic and seismic data. Because of its ability to reproduce textures so well, the coder performs very well, even at high bitrate.

In recent work, it was proposed to use lossy compression to remove noise from corrupted signals, based on the rationale that a reasonable compression method retains the dominant signal features more than the randomness of the noise. To further understand and substantiate this theory, we first explain why compression (via coefficient quantization) is appropriate for filtering noise from signal by making the connection that quantization of transform coefficients approximates the operation of wavelet thresholding for denoising. That is, denoising is mainly due to the zero-zone and that the full precision of the thresholded coefficients is of secondary importance. Secondly, under the realistic assumption that wavelet coefficients follow a Generalized Gaussian distribution, we derive an optimal threshold value (and thus the zero-zone width) from minimizing the mean squared error among soft-threshold estimators. We propose an adaptive threshold which is easy to compute and nearly o...

In this paper, we derive an asymptotically optimal multi-layer coding scheme for entropy-coded scalar quantizers (S0) that minimizes the weighted mean-squared error (WMSE). The optimal entropy-coded S0 is non-uniform in the case of WMSE. The conventional multi-layer coder quantizes the base-layer reconstruction error at the enhancement-layer, and is sub-optimal for the WMSE criterion. We consider the cornpander representation of the quantizer, and propose to implement scalability in the compressed domain. We show that such a multi-layer coding system achieves the operational rate-distortion bound given by the non-scalable entropy-coded S0, at the limit of high resolution. Simulation results for a synthetic memoryless Laplace source with/-law companding are presented for various values of layer rates. Substantial gains are also achieved on the "real-world" sources of audio signals, when the optimal multi-layer approach is applied to a two-layer scalable MPEG-4 Advanced Audio Coder.

This report considers low resolution scalar quantization. Specifically, it considers entropyconstrained scalar quantization for memoryless Gaussian and Laplacian sources with both squared and absolute error distortion measures. The slope of the operational rate-distortion functions of scalar quantization for these sources and distortion measures is found. It is shown that in three of the four cases this slope equals the slope of the corresponding Shannon rate-distortion function, which implies that asymptotic low resolution scalar quantization with entropy coding is an optimal coding technique for these three cases. For the case of a Gaussian source and absolute error distortion measure, however, the slope at rate equal zero of the operational-rate distortion function of scalar quantization is infinite, and hence does not match the slope of the corresponding Shannon rate-distortion function. Consequently, scalar quantization is not an optimal coding technique for Gaussian sources and absolute error distortion measure. The results are obtained via analysis of uniform and binary scalar quantizers, which shows that in low resolution their operational rate-distortion functions, in all four cases, are the same as the corresponding operational rate-distortion functions of scalar quantization in general. Lastly, the slope of the Shannon rate-distortion function (the function itself is not known) at rate equal zero is found for a Laplacian source and squared error distortion measure. 1

Abstract — This paper describes the low-complexity 14kHz bandwidth audio coding algorithm which has been recently standardized by ITU-T as Recommendation G.722.1 Annex C (“G.722.1C”). The algorithm is an extension to ITU-T Recommendation G.722.1 and a doubled form of the G.722.1 algorithm to permit 14 kHz audio bandwidth using a 32 kHz audio sample rate, at 24, 32, and 48 kbit/s. The G.722.1C codec features very high audio quality, extremely low computational complexity, and low algorithmic delay compared to other state-of-the-art audio coding algorithms. This codec is suitable for use in video conferencing and teleconferencing, and Internet streaming applications as well as a general-purpose 14 kHz audio codec. Subjective test results from the Characterization phase of G.722.1C are also presented in the paper. Index Terms — Audio coding, low complexity, superwideband, transform coding

2. FMRI projections on wavelet packets 3. Statistical properties of the projections

We provide an analytical study of the selection and modulus quantization of matching pursuits (MP) coefficients. We demonstrate that an optimal rate-distortion trade-off is achieved by selecting the atoms up to a dead-zone threshold, and by defining the modulus quantizer in terms of that threshold. In doing so, we take into account quantization error re-injection resulting from inserting the modulus quantizer inside the MP atom computation loop. In-loop quantization affects the stepsize of the uniform quantizer, and results in a non-uniform optimal entropy constrained quantizer. Improvements larger than one dB are obtained for video coding. 1.