On Multistage Successive Refinement for Wyner-Ziv Source Coding with Degraded Side Informations

We provide a complete characterization of the rate-distortion region for the multistage successive refinement of the Wyner-Ziv source coding problem with degraded side informations at the decoder. Necessary and sufficient conditions for a source to be successively refinable along a distortion vector are subsequently derived. A source-channel separation theorem is provided when the descriptions are sent over independent channels for the multistage case. Furthermore, we introduce the notion of generalized successive refinability with multiple degraded side informations. This notion captures whether progressive encoding to satisfy multiple distortion constraints for different side informations is as good as encoding without progressive requirement. Necessary and sufficient conditions for generalized successive refinability are given. It is shown that the following two sources are generalized successively refinable: (1) the Gaussian source with degraded Gaussian side informations, (2) the doubly symmetric binary source when the worse side information is a constant. Thus for both cases, the failure of being successively refinable is only due to the inherent uncertainty on which side information will occur at the decoder, but not the progressive encoding requirement.Comment: Submitted to IEEE Trans. Information Theory Apr. 200

Side-information Scalable Source Coding

The problem of side-information scalable (SI-scalable) source coding is considered in this work, where the encoder constructs a progressive description, such that the receiver with high quality side information will be able to truncate the bitstream and reconstruct in the rate distortion sense, while the receiver with low quality side information will have to receive further data in order to decode. We provide inner and outer bounds for general discrete memoryless sources. The achievable region is shown to be tight for the case that either of the decoders requires a lossless reconstruction, as well as the case with degraded deterministic distortion measures. Furthermore we show that the gap between the achievable region and the outer bounds can be bounded by a constant when square error distortion measure is used. The notion of perfectly scalable coding is introduced as both the stages operate on the Wyner-Ziv bound, and necessary and sufficient conditions are given for sources satisfying a mild support condition. Using SI-scalable coding and successive refinement Wyner-Ziv coding as basic building blocks, a complete characterization is provided for the important quadratic Gaussian source with multiple jointly Gaussian side-informations, where the side information quality does not have to be monotonic along the scalable coding order. Partial result is provided for the doubly symmetric binary source with Hamming distortion when the worse side information is a constant, for which one of the outer bound is strictly tighter than the other one.Comment: 35 pages, submitted to IEEE Transaction on Information Theor

Multiresolution vector quantization

Multiresolution source codes are data compression algorithms yielding embedded source descriptions. The decoder of a multiresolution code can build a source reproduction by decoding the embedded bit stream in part or in whole. All decoding procedures start at the beginning of the binary source description and decode some fraction of that string. Decoding a small portion of the binary string gives a low-resolution reproduction; decoding more yields a higher resolution reproduction; and so on. Multiresolution vector quantizers are block multiresolution source codes. This paper introduces algorithms for designing fixed- and variable-rate multiresolution vector quantizers. Experiments on synthetic data demonstrate performance close to the theoretical performance limit. Experiments on natural images demonstrate performance improvements of up to 8 dB over tree-structured vector quantizers. Some of the lessons learned through multiresolution vector quantizer design lend insight into the design of more sophisticated multiresolution codes

Incremental Refinements and Multiple Descriptions with Feedback

It is well known that independent (separate) encoding of K correlated sources may incur some rate loss compared to joint encoding, even if the decoding is done jointly. This loss is particularly evident in the multiple descriptions problem, where the sources are repetitions of the same source, but each description must be individually good. We observe that under mild conditions about the source and distortion measure, the rate ratio Rindependent(K)/Rjoint goes to one in the limit of small rate/high distortion. Moreover, we consider the excess rate with respect to the rate-distortion function, Rindependent(K, M) - R(D), in M rounds of K independent encodings with a final distortion level D. We provide two examples - a Gaussian source with mean-squared error and an exponential source with one-sided error - for which the excess rate vanishes in the limit as the number of rounds M goes to infinity, for any fixed D and K. This result has an interesting interpretation for a multi-round variant of the multiple descriptions problem, where after each round the encoder gets a (block) feedback regarding which of the descriptions arrived: In the limit as the number of rounds M goes to infinity (i.e., many incremental rounds), the total rate of received descriptions approaches the rate-distortion function. We provide theoretical and experimental evidence showing that this phenomenon is in fact more general than in the two examples above.Comment: 62 pages. Accepted in the IEEE Transactions on Information Theor

On the stability of projection methods for the incompressible Navier-Stokes equations based on high-order discontinuous Galerkin discretizations

The present paper deals with the numerical solution of the incompressible Navier-Stokes equations using high-order discontinuous Galerkin (DG) methods for discretization in space. For DG methods applied to the dual splitting projection method, instabilities have recently been reported that occur for coarse spatial resolutions and small time step sizes. By means of numerical investigation we give evidence that these instabilities are related to the discontinuous Galerkin formulation of the velocity divergence term and the pressure gradient term that couple velocity and pressure. Integration by parts of these terms with a suitable definition of boundary conditions is required in order to obtain a stable and robust method. Since the intermediate velocity field does not fulfill the boundary conditions prescribed for the velocity, a consistent boundary condition is derived from the convective step of the dual splitting scheme to ensure high-order accuracy with respect to the temporal discretization. This new formulation is stable in the limit of small time steps for both equal-order and mixed-order polynomial approximations. Although the dual splitting scheme itself includes inf-sup stabilizing contributions, we demonstrate that spurious pressure oscillations appear for equal-order polynomials and small time steps highlighting the necessity to consider inf-sup stability explicitly.Comment: 31 page

Image-based 3-D reconstruction of constrained environments

Nuclear power plays a important role to the United Kingdom electricity generation infrastructure, providing a reliable baseload of low carbon electricity. The Advanced Gas-cooled Reactor (AGR) design makes up approximately 50% of the existing fleet, however, many of the operating reactors have exceeding their original design lifetimes.To ensure safe reactor operation, engineers perform periodic in-core visual inspections of reactor components to monitor the structural health of the core as it ages. However, current inspection mechanisms deployed provide limited structural information about the fuel channel or defects.;This thesis investigates the suitability of image-based 3-D reconstruction techniques to acquire 3-D structural geometry to enable improved diagnostic and prognostic abilities for inspection engineers. The application of image-based 3-D reconstruction to in-core inspection footage highlights significant challenges, most predominantly that the image saliency proves insuffcient for general reconstruction frameworks. The contribution of the thesis is threefold. Firstly, a novel semi-dense matching scheme which exploits sparse and dense image correspondence in combination with a novel intra-image region strength approach to improve the stability of the correspondence between images.;This results in a percentage increase of 138.53% of correct feature matches over similar state-of-the-art image matching paradigms. Secondly, a bespoke incremental Structure-from-Motion (SfM) framework called the Constrained Homogeneous SfM (CH-SfM) which is able to derive structure from deficient feature spaces and constrained environments. Thirdly, the application of the CH-SfM framework to remote visual inspection footage gathered within AGR fuel channels, outperforming other state-of-the-art reconstruction approaches and extracting representative 3-D structural geometry of orientational scans and fully circumferential reconstructions.;This is demonstrated on in-core and laboratory footage, achieving an approximate 3-D point density of 2.785 - 23.8025NX/cm² for real in-core inspection footage and high quality laboratory footage respectively. The demonstrated novelties have applicability to other constrained or feature-poor environments, with future work looking to producing fully dense, photo-realistic 3-D reconstructions.Nuclear power plays a important role to the United Kingdom electricity generation infrastructure, providing a reliable baseload of low carbon electricity. The Advanced Gas-cooled Reactor (AGR) design makes up approximately 50% of the existing fleet, however, many of the operating reactors have exceeding their original design lifetimes.To ensure safe reactor operation, engineers perform periodic in-core visual inspections of reactor components to monitor the structural health of the core as it ages. However, current inspection mechanisms deployed provide limited structural information about the fuel channel or defects.;This thesis investigates the suitability of image-based 3-D reconstruction techniques to acquire 3-D structural geometry to enable improved diagnostic and prognostic abilities for inspection engineers. The application of image-based 3-D reconstruction to in-core inspection footage highlights significant challenges, most predominantly that the image saliency proves insuffcient for general reconstruction frameworks. The contribution of the thesis is threefold. Firstly, a novel semi-dense matching scheme which exploits sparse and dense image correspondence in combination with a novel intra-image region strength approach to improve the stability of the correspondence between images.;This results in a percentage increase of 138.53% of correct feature matches over similar state-of-the-art image matching paradigms. Secondly, a bespoke incremental Structure-from-Motion (SfM) framework called the Constrained Homogeneous SfM (CH-SfM) which is able to derive structure from deficient feature spaces and constrained environments. Thirdly, the application of the CH-SfM framework to remote visual inspection footage gathered within AGR fuel channels, outperforming other state-of-the-art reconstruction approaches and extracting representative 3-D structural geometry of orientational scans and fully circumferential reconstructions.;This is demonstrated on in-core and laboratory footage, achieving an approximate 3-D point density of 2.785 - 23.8025NX/cm² for real in-core inspection footage and high quality laboratory footage respectively. The demonstrated novelties have applicability to other constrained or feature-poor environments, with future work looking to producing fully dense, photo-realistic 3-D reconstructions

AirSync: Enabling Distributed Multiuser MIMO with Full Spatial Multiplexing

The enormous success of advanced wireless devices is pushing the demand for higher wireless data rates. Denser spectrum reuse through the deployment of more access points per square mile has the potential to successfully meet the increasing demand for more bandwidth. In theory, the best approach to density increase is via distributed multiuser MIMO, where several access points are connected to a central server and operate as a large distributed multi-antenna access point, ensuring that all transmitted signal power serves the purpose of data transmission, rather than creating "interference." In practice, while enterprise networks offer a natural setup in which distributed MIMO might be possible, there are serious implementation difficulties, the primary one being the need to eliminate phase and timing offsets between the jointly coordinated access points. In this paper we propose AirSync, a novel scheme which provides not only time but also phase synchronization, thus enabling distributed MIMO with full spatial multiplexing gains. AirSync locks the phase of all access points using a common reference broadcasted over the air in conjunction with a Kalman filter which closely tracks the phase drift. We have implemented AirSync as a digital circuit in the FPGA of the WARP radio platform. Our experimental testbed, comprised of two access points and two clients, shows that AirSync is able to achieve phase synchronization within a few degrees, and allows the system to nearly achieve the theoretical optimal multiplexing gain. We also discuss MAC and higher layer aspects of a practical deployment. To the best of our knowledge, AirSync offers the first ever realization of the full multiuser MIMO gain, namely the ability to increase the number of wireless clients linearly with the number of jointly coordinated access points, without reducing the per client rate.Comment: Submitted to Transactions on Networkin

Fully-Automatic Multiresolution Idealization for Filtered Ion Channel Recordings: Flickering Event Detection

We propose a new model-free segmentation method, JULES, which combines recent statistical multiresolution techniques with local deconvolution for idealization of ion channel recordings. The multiresolution criterion takes into account scales down to the sampling rate enabling the detection of flickering events, i.e., events on small temporal scales, even below the filter frequency. For such small scales the deconvolution step allows for a precise determination of dwell times and, in particular, of amplitude levels, a task which is not possible with common thresholding methods. This is confirmed theoretically and in a comprehensive simulation study. In addition, JULES can be applied as a preprocessing method for a refined hidden Markov analysis. Our new methodolodgy allows us to show that gramicidin A flickering events have the same amplitude as the slow gating events. JULES is available as an R function jules in the package clampSeg