rate distortion optimal fast thresholding with complete jpeg mpeg decoder compatibility we show a rate distortion optimal way to threshold or drop the dct coefficients of the jpeg and mpeg compression standards our optimal algorithm uses a fast dynamic programming recursive structure the primary advantage of our approach lies in its complete compatibility with standard jpeg and mpeg decoders

social networks evolving graphs with memory dependent edges abstract the plethora of digital communication technologies and their mass take up has resulted in a wealth of interest in social network data collection and analysis in recent years within many such networks the interactions are transient thus those networks evolve over time in this paper we introduce a class of models for such networks using evolving graphs with memory dependent edges which may appear and disappear according to their recent history we consider time discrete and time continuous variants of the model we consider the long term asymptotic behaviour as a function of parameters controlling the memory dependence in particular we show that such networks may continue evolving forever or else may quench and become static containing immortal and or extinct edges this depends on the existence or otherwise of certain infinite products and series involving age dependent model parameters we show how to differentiate between the alternatives based on a finite set of observations to test these ideas we show how model parameters may be calibrated based on limited samples of time dependent data and we apply these concepts to three real networks summary data on mobile phone use from a developing region online social business network data from china and disaggregated mobile phone communications data from a reality mining experiment in the us in each case we show that there is evidence for memory dependent dynamics such as that embodied within the class of models proposed here

joint optimization of run length coding huffman coding and quantization table with complete baseline jpeg decoder compatibility to maximize rate distortion performance while remaining faithful to the jpeg syntax the joint optimization of the huffman tables quantization step sizes and dct indices of a jpeg encoder is investigated given huffman tables and quantization step sizes an efficient graph based algorithm is first proposed to find the optimal dct indices in the form of run size pairs based on this graph based algorithm an iterative algorithm is then presented to jointly optimize run length coding huffman coding and quantization table selection the proposed iterative algorithm not only results in a compressed bitstream completely compatible with existing jpeg and mpeg decoders but is also computationally efficient furthermore when tested over standard test images it achieves the best jpeg compression results to the extent that its own jpeg compression performance even exceeds the quoted psnr results of some state of the art wavelet based image coders such as shapiro s embedded zerotree wavelet algorithm at the common bit rates under comparison both the graph based algorithm and the iterative algorithm can be applied to application areas such as web image acceleration digital camera image compression mpeg frame optimization and transcoding etc

expander graphs and their applications a major consideration we had in writing this survey was to make it accessible to mathematicians as well as to computer scientists since expander graphs the protagonists of our story come up in numerous and often surprising contexts in both fields but perhaps we should start with a few words about graphs in general they are of course one of the prime objects of study in discrete mathematics however graphs are among the most ubiquitous models of both natural and human made structures in the natural and social sciences they model relations among species societies companies etc in computer science they represent networks of communication data organization computational devices as well as the flow of computation and more in mathematics cayley graphs are useful in group theory graphs carry a natural metric and are therefore useful in geometry and though they are just one dimensional complexes they are useful in certain parts of topology e g knot theory in statistical physics graphs can represent local connections between interacting parts of a system as well as the dynamics of a physical process on such systems the study of these models calls then for the comprehension of the significant structural properties of the relevant graphs but are there nontrivial structural properties which are universally important expansion of a graph requires that it is simultaneously sparse and highly connected expander graphs were first defined by bassalygo and pinsker and their existence first proved by pinsker in the early 70s the property of being an expander seems significant in many of these mathematical computational and physical contexts it is not surprising that expanders are useful in the design and analysis of communication networks what is less obvious is that expanders have surprising utility in other computational settings such as in the theory of error correcting codes and the theory of pseudorandomness in mathematics we will encounter e g their role in the study of metric embeddings and in particular in work around the baum connes conjecture expansion is closely related to the convergence rates of markov chains and so they play a key role in the study of monte carlo algorithms in statistical mechanics and in a host of practical computational applications the list of such interesting and fruitful connections goes on and on with so many applications we will not even

motion estimation methods for overlapped block motion compensation an extension of conventional block motion compensation bmc overlapped block motion compensation obmc has been shown to reduce residual errors and blocking effects in motion compensated video however the overlap creates a noncausal spatial dependence between blocks and complicates motion estimation me for obmc iterative methods have traditionally been employed for overlapped block motion estimation obme for compression the rate for the motion vector field mvf may also be constrained this work considers several rate constrained obme algorithms both iterative and noniterative experiments demonstrate that a simple raster scan algorithm is effective as a suboptimal noniterative solution with comparable or better rate distortion performance and computational complexity than iterative obme algorithms depending on the application either this method or a simple block matching algorithm plus iteration are the most attractive of the tested obme schemes

boolean compressed sensing and noisy group testing the fundamental task of group testing is to recover a small distinguished subset of items from a large population while efficiently reducing the total number of tests measurements the key contribution of this paper is in adopting a new information theoretic perspective on group testing problems we formulate the group testing problem as a channel coding decoding problem and derive a single letter characterization for the total number of tests used to identify the defective set although the focus of this paper is primarily on group testing our main result is generally applicable to other compressive sensing models

subband coding systems incorporating quantizer models a new method for dealing with the effects of quantization in a subband system is proposed it uses the gain plus additive noise linear model for the lloyd max quantizer based on this it is demonstrated how by an appropriate choice of synthesis filters one can cancel all signal dependent errors at the output of the system the only remaining error is random in nature and not correlated with the input signal we therefore have a tradeoff between the error being only random or having signal dependent components as well since the error variances in both cases are comparable as a result of having only a random error it is possible to reduce this error using for example a noise removal technique the result is then extended to the case where the input is a multidimensional signal and arbitrary sampling lattices are used as well as to the qmf alias cancellation case to demonstrate the validity of the proposed approach two types of experiments on images are carried out in a toy example it is shown that using noise removal could be beneficial for a more realistic coding scheme however it is demonstrated that even in the case when the model is no longer valid when some of the subbands are discarded the output error is still much less correlated with the input signal as opposed to the commonly used subband system while visually the reconstructed images look very similar

approximate counting uniform generation and rapidly mixing markov chains the paper studies effective approximate solutions to combinatorial counting and uniform generation problems using a technique based on the simulation of ergodic markov chains it is shown that for self reducible structures almost uniform generation is possible in polynomial time provided only that randomised approximate counting to within some arbitrary polynomial factor is possible in polynomial time it follows that for self reducible structures polynomial time randomised algorithms for counting to within factors of the form 1 n are available either for all fl e r or for no fi e r a substantial part of the paper is devoted to investigating the rate of convergence of finite ergodic markov chains and a simple but powerful characterisation of rapid convergence for a broad class of chains based on a structural property of the underlying graph is established finally the general techniques of the paper are used to derive an almost uniform generation procedure for labelled graphs with a given degree sequence which is valid over a much wider range of degrees than previous methods this in turn leads to randomised approximate counting algorithms for these graphs with very good

communicability in complex networks we propose a new measure of the communicability of a complex network which is a broad generalization of the concept of the shortest path according to the new measure most of the real world networks display the largest communicability between the most connected popular nodes of the network assortative communicability there are also several networks with the disassortative communicability where the most popular nodes communicate very poorly to each other using this information we classify a diverse set of real world complex systems into a small number of universality classes based on their structure dynamic correlation in addition the new communicability measure is able to distinguish finer structures of networks such as communities into which a network is divided a community is unambiguously defined here as a set of nodes displaying larger communicability among them than to the rest of the nodes in the network

range dependent random graphs and their application to modeling large small world proteome datasets in this paper we consider the problem of characterizing and modeling large scale networks using classes of range dependent graphs which possess appropriate small world properties the application we have in mind is to bioinformatics where methods of rapid protein identification mean that such proteome datasets listing various observed protein protein associations will become more and more prevalent we introduce a class of range dependent graphs governed by a power law relating intervertex range to edge probability which are amenable to analysis and for which macroscopic graph parameters are given by explicit forms we show how these may be employed in representing a given network using a maximum likelihood approach this in turn annotates every given edge with its range representing the tendency for such an association to be transitive we apply this technique to published proteome data and demonstrate that known protein associations are thus identified

lossless near lossless and refinement coding of bilevel images we present general and unified algorithms for lossy lossless coding of bilevel images the compression is realized by applying arithmetic coding to conditional probabilities as in the current jbig standard the conditioning may be specified by a template for better compression the more general free tree may be used loss may be introduced in a preprocess on the encoding side to increase compression the primary algorithm is a rate distortion controlled greedy flipping of pixels though being general the algorithms are primarily aimed at material containing half toned images as a supplement to the specialized soft pattern matching techniques that work better for text template based refinement coding is applied for lossy to lossless refinement introducing only a small amount of loss in half toned test images compression is increased by up to a factor of four compared with jbig lossy lossless and refinement decoding speed and lossless encoding speed are less than a factor of two slower than jbig the de coding method is proposed as part of jbig2 an emerging international standard for lossless lossy compression of bilevel images

an embedded still image coder with rate distortion optimization it is well known that the fixed rate coder achieves optimality when all coefficients are coded with the same rate distortion r d slope in this paper we show that the performance of the embedded coder can be optimized in a rate distortion sense by coding the coefficients with decreasing r d slope we denote such a coding strategy as rate distortion optimized embedding rde rde allocates the available coding bits first to the coefficient with the steepest r d slope i e the largest distortion decrease per coding bit the resultant coding bitstream can be truncated at any point and still maintain an optimal r d performance to avoid the overhead of coding order transmission we use the expected r d slope which can be calculated from the coded bits and is available in both the encoder and the decoder with the probability estimation table of the qm coder the calculation of the r d slope can be just a lookup table operation experimental results show that the rate distortion optimization significantly improves the coding efficiency in a wide bit rate range

graph constrained group testing nonadaptive group testing involves grouping arbitrary subsets of n items into different pools each pool is then tested and defective items are identified a fundamental question involves minimizing the number of pools required to identify at most d defective items motivated by applications in network tomography sensor networks and infection propagation a variation of group testing problems on graphs is formulated unlike conventional group testing problems each group here must conform to the constraints imposed by a graph for instance items can be associated with vertices and each pool is any set of nodes that must be path connected in this paper a test is associated with a random walk in this context conventional group testing corresponds to the special case of a complete graph on n vertices for interesting classes of graphs a rather surprising result is obtained namely that the number of tests required to identify d defective items is substantially similar to what is required in conventional group testing problems where no such constraints on pooling is imposed specifically if t n corresponds to the mixing time of the graph g it is shown that with m o d2t2 n log n d nonadaptive tests one can identify the defective items consequently for the erdos renyi random graph g n p as well as expander graphs with constant spectral gap it follows that m o d2 log3 n non adaptive tests are sufficient to identify d defective items next a specific scenario is considered that arises in network tomography for which it is shown that m o d3 log3 n nonadaptive tests are sufficient to identify d defective items noisy counterparts of the graph constrained group testing problem are considered for which parallel results are developed we also briefly discuss extensions to compressive sensing on graphs

lossless image compression by quantization feedback in a content driven enhanced laplacian pyramid in this paper the effects of quantization noise feedback on the entropy of laplacian pyramids are investigated this technique makes it possible for the maximum absolute reconstruction error to be easily and strongly upper bounded near lossless coding and therefore allows reversible compression the entropy minimizing optimum quantizer is obtained by modeling the first order distributions of the differential signals as laplacian densities and by deriving a model for the equivalent memoryless entropy a novel approach based on an enhanced laplacian pyramid is proposed for the compression either lossless or lossy of gray scale images major details are prioritized through a content driven decision rule embedded in a uniform threshold quantizer with noise feedback lossless coding shows improvements over reversible joint photographers expert group jpeg and the reduced difference pyramid schemes while lossy coding outperforms jpeg with a significant peak signal to noise ratio psnr gain also subjective quality is higher even at very low bit rates due to the absence of the annoying impairments typical of jpeg moreover image versions having resolution and snr that are both progressively increasing are made available at the receiving end from the earliest retrieval stage on as intermediate steps of the decoding procedure without any additional cost

joint thresholding and quantizer selection for transform image coding entropy constrained analysis and applications to baseline jpeg striving to maximize baseline joint photographers expert group jpeg image quality without compromising compatibility of current jpeg decoders we develop an image adaptive jpeg encoding algorithm that jointly optimizes quantizer selection coefficient thresholding and huffman coding within a rate distortion r d framework practically speaking our algorithm unifies two previous approaches to image adaptive jpeg encoding r d optimized quantizer selection and r d optimal thresholding conceptually speaking our algorithm is a logical consequence of entropy constrained vector quantization ecvq design principles in the severely constrained instance of jpeg compatible encoding we explore both viewpoints the practical to concretely derive our algorithm and the conceptual to justify the claim that our algorithm approaches the best performance that a jpeg encoder can achieve this performance includes significant objective peak signal to noise ratio psnr improvement over previous work and at high rates gives results comparable to state of the art image coders for example coding the lena image at 1 0 b pixel our jpeg encoder achieves a psnr performance of 39 6 db that slightly exceeds the quoted psnr results of shapiro s wavelet based zero tree coder using a visually based distortion metric we can achieve noticeable subjective improvement as well furthermore our algorithm may be applied to other systems that use run length encoding including intraframe mpeg and subband or wavelet coding

optimal trellis based buffered compression and fast approximations the authors formalize the description of the buffer constrained adaptive quantization problem for a given set of admissible quantizers used to code a discrete nonstationary signal sequence in a buffer constrained environment they formulate the optimal solution they also develop slightly suboptimal but much faster approximations these solutions are valid for any globally minimum distortion criterion which is additive over the individual elements of the sequence as a first step they define the problem as one of constrained discrete optimization and establish its equivalence to some of the problems studied in the field of integer programming forward dynamic programming using the viterbi algorithm is shown to provide a way of computing the optimal solution then they provide a heuristic algorithm based on lagrangian optimization using an operational rate distortion framework that with computing complexity reduced by an order of magnitude approaches the optimally achievable performance the algorithms can serve as a benchmark for assessing the performance of buffer control strategies and are useful for applications such as multimedia workstation displays video encoding for cd roms and buffered jpeg coding environments where processing delay is not a concern but decoding buffer size has to be minimized

an optimal polygonal boundary encoding scheme in the rate distortion sense in this paper we present fast and efficient methods for the lossy encoding of object boundaries that are given as eight connect chain codes we approximate the boundary by a polygon and consider the problem of finding the polygon which leads to the smallest distortion for a given number of bits we also address the dual problem of finding the polygon which leads to the smallest bit rate for a given distortion we consider two different classes of distortion measures the first class is based on the maximum operator and the second class is based on the summation operator for the first class we derive a fast and optimal scheme that is based on a shortest path algorithm for a weighted directed acyclic graph for the second class we propose a solution approach that is based on the lagrange multiplier method which uses the above mentioned shortest path algorithm since the lagrange multiplier method can only find solutions on the convex hull of the operational rate distortion function we also propose a tree pruning based algorithm that can find all the optimal solutions finally we present results of the proposed schemes using objects from the miss america sequence

bit allocation for dependent quantization with applications to multiresolution and mpeg video coders we address the problem of efficient bit allocation in a dependent coding environment while optimal bit allocation for independently coded signal blocks has been studied in the literature we extend these techniques to the more general temporally and spatially dependent coding scenarios of particular interest are the topical mpeg video coder and multiresolution coders our approach uses an operational rate distortion r d framework for arbitrary quantizer sets we show how a certain monotonicity property of the dependent r d curves can be exploited in formulating fast ways to obtain optimal and near optimal solutions we illustrate the application of this property in specifying intelligent pruning conditions to eliminate suboptimal operating points for the mpeg allocation problem for which we also point out fast nearly optimal heuristics additionally we formulate an efficient allocation strategy for multiresolution coders using the spatial pyramid coder as an example we then extend this analysis to a spatio temporal 3 d pyramidal coding scheme we tackle the compatibility problem of optimizing full resolution quality while simultaneously catering to subresolution bit rate or quality constraints we show how to obtain fast solutions that provide nearly optimal typically within 0 3 db full resolution quality while providing much better performance for the subresolution layer typically 2 3 db better than the full resolution optimal solution

best wavelet packet bases in a rate distortion sense a fast rate distortion r d optimal scheme for coding adaptive trees whose individual nodes spawn descendents forming a disjoint and complete basis cover for the space spanned by their parent nodes is presented the scheme guarantees operation on the convex hull of the operational r d curve and uses a fast dynamic programing pruning algorithm to markedly reduce computational complexity applications for this coding technique include r coefman et al s yale univ 1990 generalized multiresolution wavelet packet decomposition iterative subband coders and quadtree structures applications to image processing involving wavelet packets as well as discrete cosine transform dct quadtrees are presented

optimal buffered compression and coding mode selection for mpeg 4 shape coding we propose an optimal buffered compression algorithm for shape coding as defined in the forthcoming mpeg 4 international standard the mpeg 4 shape coding scheme consists of two steps first distortion is introduced by down and up scaling then context based arithmetic encoding is applied since arithmetic coding is lossless the down up scaling step is considered as a virtual quantizer we first formulate the buffer constrained adaptive quantization problem for shape coding and then propose an algorithm for the optimal solution under buffer constraints previously the fact that a conversion ratio cr of 1 4 makes a coded image irritating to human observers for qcif size was reported for mpeg 4 shape coding therefore careful consideration for small size images such as qcif should be given to prevent coded images from being unacceptable to this end a low bit rate tuned algorithm is proposed in this paper as well experimental results are given using an mpeg 4 shape codec

the laplacian pyramid as a compact image code we describe a technique for image encoding in which local operators of many scales but identical shape serve as the basis functions the representation differs from established techniques in that the code elements are localized in spatial frequency as well as in space pixel to pixel correlations are first removed by subtracting a lowpass filtered copy of the image from the image itself the result is a net data compression since the difference or error image has low variance and entropy and the low pass filtered image may represented at reduced sample density further data compression is achieved by quantizing the difference image these steps are then repeated to compress the low pass image iteration of the process at appropriately expanded scales generates a pyramid data structure the encoding process is equivalent to sampling the image with laplacian operators of many scales thus the code tends to enhance salient image features a further advantage of the present code is that it is well suited for many image analysis tasks as well as for image compression fast algorithms are described for coding and decoding

optimization of mpeg 2 snr scaleable codecs it is shown how the signal to noise snr scaleable coder can benefit from optimizing quantified discrete cosine transform dct coefficients in a rate distortion context in order to reduce bit rate overheads the technique is based on adjusting the quantized coefficients rather than dropping them since the former gives finer control over rate distortion trade offs the widely used lagrangian optimization technique is then applied to arrive at the optimally adjusted coefficients block we show that such an optimization is very efficient for the second layer but has little effect on the base layer

an operational rate distortion optimal single pass snr scalable video coder we introduce a new methodology for signal to noise ratio snr video scalability based on the partitioning of the dct coefficients the dct coefficients of the displaced frame difference dfd for inter blocks or the intensity for intra blocks are partitioned into a base layer and one or more enhancement layers thus producing an embedded bitstream subsets of this bitstream can be transmitted with increasing video quality as measured by the snr given a bit budget for the base and enhancement layers the partitioning of the dct coefficients is done in a way that is optimal in the operational rate distortion sense the optimization is performed using lagrangian relaxation and dynamic programming dp experimental results are presented and conclusions are drawn

born again group testing multiaccess communications a brief summary of the basic notions of group testing is presented together with a brief historical account one of the early papers on group testing is shown to include a description of the tree search polling algorithm of hayes the classical group testing problem is formulated including a criterion for optimality of test plans a restricted class of tests called nested testing is described and a complete description for an optimal nested strategy is given for both a finite number and an infinite number of bernoulli distributed random variables a generalization of group testing applicable to the random access communications problem is presented

rate distortion optimization for h 264 interframe coding a general framework and algorithms rate distortion rd optimization for h 264 interframe coding with complete baseline decoding compatibility is investigated on a frame basis using soft decision quantization sdq rather than the standard hard decision quantization we first establish a general framework in which motion estimation quantization and entropy coding in h 264 for the current frame can be jointly designed to minimize a true rd cost given previously coded reference frames we then propose three rd optimization algorithms a graph based algorithm for near optimal sdq in h 264 baseline encoding given motion estimation and quantization step sizes an algorithm for near optimal residual coding in h 264 baseline encoding given motion estimation and an iterative overall algorithm to optimize h 264 baseline encoding for each individual frame given previously coded reference frames with them embedded in the indicated order the graph based algorithm for near optimal sdq is the core given motion estimation and quantization step sizes it is guaranteed to perform optimal sdq if the weak adjacent block dependency utilized in the context adaptive variable length coding of h 264 is ignored for optimization the proposed algorithms have been implemented based on the reference encoder jm82 of h 264 with complete compatibility to the baseline profile experiments show that for a set of typical video testing sequences the graph based algorithm for near optimal sdq the algorithm for near optimal residual coding and the overall algorithm achieve on average 6 8 and 12 respectively rate reduction at the same psnr ranging from 30 to 38 db when compared with the rd optimization method implemented in the h 264 reference software

detect local communities in networks with an outside rate coefficient abstract in this paper we present a local method for detecting communities in networks we define an outside rate coefficient o u t in our method o u t has a very simple form and is easy to calculate the local community enclosing a starting node can be detected by agglomerating the node with the smallest o u t at each time step when there are two or more nodes having the same smallest outside rate coefficient o u t we agglomerate the node with the largest k i n this operation is remarkably beneficial to the accuracy of our method and simulations on benchmark networks and real networks demonstrate that our local method is efficient to detect communities in networks