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Distributed compressed sensing
, 2005
"... Compressed sensing is an emerging field based on the revelation that a small collection of linear projections of a sparse signal contains enough information for reconstruction. In this paper we introduce a new theory for distributed compressed sensing (DCS) that enables new distributed coding algori ..."
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Cited by 84 (21 self)
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Compressed sensing is an emerging field based on the revelation that a small collection of linear projections of a sparse signal contains enough information for reconstruction. In this paper we introduce a new theory for distributed compressed sensing (DCS) that enables new distributed coding algorithms for multisignal ensembles that exploit both intra and intersignal correlation structures. The DCS theory rests on a new concept that we term the joint sparsity of a signal ensemble. We study in detail three simple models for jointly sparse signals, propose algorithms for joint recovery of multiple signals from incoherent projections, and characterize theoretically and empirically the number of measurements per sensor required for accurate reconstruction. We establish a parallel with the SlepianWolf theorem from information theory and establish upper and lower bounds on the measurement rates required for encoding jointly sparse signals. In two of our three models, the results are asymptotically bestpossible, meaning that both the upper and lower bounds match the performance of our practical algorithms. Moreover, simulations indicate that the asymptotics take effect with just a moderate number of signals. In some sense DCS is a framework for distributed compression of sources with memory, which has remained a challenging problem for some time. DCS is immediately applicable to a range of problems in sensor networks and arrays.
Context tree estimation for not necessarily finite memory processes, via BIC and MDL
 IEEE Trans. Inf. Theory
, 2006
"... The concept of context tree, usually defined for finite memory processes, is extended to arbitrary stationary ergodic processes (with finite alphabet). These context trees are not necessarily complete, and may be of infinite depth. The familiar BIC and MDL principles are shown to provide strongly co ..."
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Cited by 25 (1 self)
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The concept of context tree, usually defined for finite memory processes, is extended to arbitrary stationary ergodic processes (with finite alphabet). These context trees are not necessarily complete, and may be of infinite depth. The familiar BIC and MDL principles are shown to provide strongly consistent estimators of the context tree, via optimization of a criterion for hypothetical context trees of finite depth, allowed to grow with the sample size n as o(log n). Algorithms are provided to compute these estimators in O(n) time, and to compute them online for all i ≤ n in o(n log n) time.
Schemes for BiDirectional Modeling of Discrete Stationary Sources
, 2005
"... Adaptive models are developed to deal with bidirectional modeling of unknown discrete stationary sources, which can be generally applied to statistical inference problems such as noncausal universal discrete denoising that exploits bidirectional dependencies. Efficient algorithms for constructing ..."
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Cited by 14 (9 self)
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Adaptive models are developed to deal with bidirectional modeling of unknown discrete stationary sources, which can be generally applied to statistical inference problems such as noncausal universal discrete denoising that exploits bidirectional dependencies. Efficient algorithms for constructing those models are developed and implemented. Denoising is a primary focus of the application of those models, and we compare their performance to that of the DUDE algorithm [1] for universal discrete denoising.
Linear Time Universal Coding and Time Reversal of Tree Sources via FSM Closure
 IEEE Trans. Inform. Theory
, 2004
"... Tree models are efficient parametrizations of finitememory processes, offering potentially significant model cost savings. The information theory literature has focused mostly on redundancy aspects of the universal estimation and coding of these models. In this paper, we investigate representations ..."
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Cited by 13 (2 self)
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Tree models are efficient parametrizations of finitememory processes, offering potentially significant model cost savings. The information theory literature has focused mostly on redundancy aspects of the universal estimation and coding of these models. In this paper, we investigate representations and supporting data structures for finitememory processes, as well as the major impact these structures have on the computational complexity of the universal algorithms in which they are used. We first generalize the class of tree models, and then define and investigate the properties of the finite state machine (FSM) closure of a tree, which is the smallest FSM that generates all the processes generated by the tree. The interaction between FSM closures, generalized context trees, and classical data structures such as compact suffix trees brings together the informationtheoretic and the computational aspects, leading to an implementation in linear encoding/decoding time of the semipredictive approach to the Context algorithm, a lossless universal coding scheme in the class of tree models. An optimal context selection rule and the corresponding context transitions are computationally not more expensive than the various steps involved in the implementation of the BurrowsWheeler transform (BWT) and use, in fact, similar tools. We also present a reversible transform that displays the same "context deinterleaving" feature as the BWT but is naturally based on an optimal context tree. FSM closures are also applied to an investigation of the effect of time reversal on tree models, motivated in part by the following question: When compressing a data sequence using a universal scheme in the class of tree models, can it make a difference whether we read the sequence from...
Antisequential Suffix Sorting For BWTBase Data Compression
 IEEE Transactions on Computers
, 2005
"... Abstract—Suffix sorting requires ordering all suffixes of all symbols in an input sequence and has applications in running queries on large texts and in universal lossless data compression based on the Burrows Wheeler transform (BWT). We propose a new suffix lists data structure that leads to three ..."
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Cited by 4 (0 self)
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Abstract—Suffix sorting requires ordering all suffixes of all symbols in an input sequence and has applications in running queries on large texts and in universal lossless data compression based on the Burrows Wheeler transform (BWT). We propose a new suffix lists data structure that leads to three fast, antisequential, and memoryefficient algorithms for suffix sorting. For a lengthN input over a sizejXj alphabet, the worstcase complexities of these algorithms are ðN2Þ, OðjXjN logð N ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi jXjÞÞ, and OðN jXj logð N jXjÞ q Þ, respectively. Furthermore, simulation results indicate performance that is competitive with other suffix sorting methods. In contrast, the suffix sorting methods that are fastest on standard test corpora have poor worstcase performance. Therefore, in comparison with other suffix sorting methods, suffix lists offer a useful trade off between practical performance and worstcase behavior. Another distinguishing feature of suffix lists is that these algorithms are simple; some of them can be implemented in VLSI. This could accelerate suffix sorting by at least an order of magnitude and enable highspeed BWTbased compression systems.
Nearly tight bounds on the encoding length of the BurrowsWheeler transform
 In Proc. Work. on Analytical Algorithmics and Combinatorics, January 2008. Indexing, and Retrieval for Massive String Data 13
"... In this paper, we present a nearly tight analysis of the encoding length of the BurrowsWheeler Transform (bwt) that is motivated by the text indexing setting. For a text T of n symbols drawn from an alphabet Σ, our encoding scheme achieves bounds in terms of the hthorder empirical entropy Hh of th ..."
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Cited by 1 (1 self)
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In this paper, we present a nearly tight analysis of the encoding length of the BurrowsWheeler Transform (bwt) that is motivated by the text indexing setting. For a text T of n symbols drawn from an alphabet Σ, our encoding scheme achieves bounds in terms of the hthorder empirical entropy Hh of the text, and takes linear time for encoding and decoding. We also describe a lower bound on the encoding length of the bwt that constructs an infinite (nontrivial) class of texts that are among the hardest to compress using the bwt. We then show that our upper bound encoding length is nearly tight with this lower bound for the class of texts we described. In designing our bwt encoding and its lower bound, we also address the tsubset problem; here, the goal is to store a subset of t items drawn from a universe [1..n] using just lg () n t +O(1) bits of space. A number of solutions to this basic problem are known, however encoding or decoding usually requires either O(t) operations on large integers [Knu05, Rus05] or O(n) operations. We provide a novel approach to reduce the encoding/decoding time to just O(t) operations on small integers (of size O(lg n) bits), without increasing the space required. 1