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47
A Panorama on Multiscale Geometric Representations, Intertwining Spatial, Directional and Frequency Selectivity
, 2011
"... The richness of natural images makes the quest for optimal representations in image processing and computer vision challenging. The latter observation has not prevented the design of image representations, which trade off between efficiency and complexity, while achieving accurate rendering of smoot ..."
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Cited by 16 (7 self)
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The richness of natural images makes the quest for optimal representations in image processing and computer vision challenging. The latter observation has not prevented the design of image representations, which trade off between efficiency and complexity, while achieving accurate rendering of smooth regions as well as reproducing faithful contours and textures. The most recent ones, proposed in the past decade, share an hybrid heritage highlighting the multiscale and oriented nature of edges and patterns in images. This paper presents a panorama of the aforementioned literature on decompositions in multiscale, multiorientation bases or dictionaries. They typically exhibit redundancy to improve sparsity in the transformed domain and sometimes its invariance with respect to simple geometric deformations (translation, rotation). Oriented multiscale dictionaries extend traditional wavelet processing and may offer rotation invariance. Highly redundant dictionaries require specific algorithms to simplify the search for an efficient (sparse) representation. We also discuss the extension of multiscale geometric decompositions to nonEuclidean domains such as the sphere or arbitrary meshed surfaces. The etymology of panorama suggests an overview, based on a choice of partially overlapping “pictures”.
Frequencydomain design of overcomplete rationaldilation wavelet transforms
 IEEE Trans. on Signal Processing
, 2009
"... The dyadic wavelet transform is an effective tool for processing piecewise smooth signals; however, its poor frequency resolution (its low Qfactor) limits its effectiveness for processing oscillatory signals like speech, EEG, and vibration measurements, etc. This paper develops a more flexible fami ..."
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Cited by 10 (5 self)
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The dyadic wavelet transform is an effective tool for processing piecewise smooth signals; however, its poor frequency resolution (its low Qfactor) limits its effectiveness for processing oscillatory signals like speech, EEG, and vibration measurements, etc. This paper develops a more flexible family of wavelet transforms for which the frequency resolution can be varied. The new wavelet transform can attain higher Qfactors (desirable for processing oscillatory signals) or the same low Qfactor of the dyadic wavelet transform. The new wavelet transform is modestly overcomplete and based on rational dilations. Like the dyadic wavelet transform, it is an easily invertible ‘constantQ’ discrete transform implemented using iterated filter banks and can likewise be associated with a wavelet frame for L2(R). The wavelet can be made to resemble a Gabor function and can hence have good concentration in the timefrequency plane. The construction of the new wavelet transform depends on the judicious use of both the transform’s redundancy and the flexibility allowed by frequencydomain filter design. I.
Compressive sampling of swallowing accelerometry signals using timefrequency dictionaries based on modulated discrete prolate spheroidal sequences
 EURASIP Journal on Advances in Signal Processing
, 2012
"... Monitoring physiological functions such as swallowing often generates large volumes of samples to be stored and processed, which can introduce computational constraints especially if remote monitoring is desired. In this paper, we propose a compressive sensing (CS) algorithm to alleviate some of th ..."
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Cited by 9 (2 self)
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Monitoring physiological functions such as swallowing often generates large volumes of samples to be stored and processed, which can introduce computational constraints especially if remote monitoring is desired. In this paper, we propose a compressive sensing (CS) algorithm to alleviate some of these issues while acquiring dualaxis swallowing accelerometry signals. The proposed CS approach uses a timefrequency dictionary where the members are modulated discrete prolate spheroidal sequences (MDPSS). These waveforms are obtained by modulation and variation of discrete prolate spheroidal sequences (DPSS) in order to reflect the timevarying nature of swallowing acclerometry signals. While the modulated bases permit one to represent the signal behavior accurately, the matching pursuit algorithm is adopted to iteratively decompose the signals into an expansion of the dictionary bases. To test the accuracy of the proposed scheme, we carried out several numerical experiments with synthetic test signals and dualaxis swallowing accelerometry signals. In both cases, the proposed CS approach based on the MDPSS yields more accurate representations than the CS approach based on DPSS. Specifically, we show that dualaxis swallowing accelerometry signals can be accurately reconstructed
Sparse representation for target detection in hyperspectral imagery
 IEEE J. Sel. Topics Signal Process
"... Abstract—In this paper, we propose a new sparsitybased algorithm for automatic target detection in hyperspectral imagery (HSI). This algorithm is based on the concept that a pixel in HSI lies in a lowdimensional subspace and thus can be represented as a sparse linear combination of the training sa ..."
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Cited by 9 (4 self)
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Abstract—In this paper, we propose a new sparsitybased algorithm for automatic target detection in hyperspectral imagery (HSI). This algorithm is based on the concept that a pixel in HSI lies in a lowdimensional subspace and thus can be represented as a sparse linear combination of the training samples. The sparse representation (a sparse vector corresponding to the linear combination of a few selected training samples) of a test sample can be recovered by solving an 0norm minimization problem. With the recent development of the compressed sensing theory, such minimization problem can be recast as a standard linear programming problem or efficiently approximated by greedy pursuit algorithms. Once the sparse vector is obtained, the class of the test sample can be determined by the characteristics of the sparse vector on reconstruction. In addition to the constraints on sparsity and reconstruction accuracy, we also exploit the fact that in HSI the neighboring pixels have a similar spectral characteristic (smoothness). In our proposed algorithm, a smoothness constraint is also imposed by forcing the vector Laplacian at each reconstructed pixel to be minimum all the time within the minimization process. The proposed sparsitybased algorithm is applied to several hyperspectral imagery to detect targets of interest. Simulation results show that our algorithm outperforms the classical hyperspectral target detection algorithms, such as the popular spectral matched filters, matched subspace detectors, adaptive subspace detectors, as well as binary classifiers such as support vector machines. Index Terms—Hyperspectral imagery, sparse recovery, sparse representation, spatial correlation, target detection. I.
MultipleBases BeliefPropagation Decoding of HighDensity Cyclic Codes
, 2009
"... We introduce a new method for decoding short and moderate length linear block codes with dense paritycheck matrix representations of cyclic form, termed multiplebases beliefpropagation (MBBP). The proposed iterative scheme makes use of the fact that a code has many structurally diverse parityche ..."
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Cited by 6 (2 self)
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We introduce a new method for decoding short and moderate length linear block codes with dense paritycheck matrix representations of cyclic form, termed multiplebases beliefpropagation (MBBP). The proposed iterative scheme makes use of the fact that a code has many structurally diverse paritycheck matrices, capable of detecting different error patterns. We show that this inherent code property leads to decoding algorithms with significantly better performance when compared to standard BP decoding. Furthermore, we describe how to choose sets of paritycheck matrices of cyclic form amenable for multiplebases decoding, based on analytical studies performed for the binary erasure channel. For several cyclic and extended cyclic codes, the MBBP decoding performance can be shown to closely follow that of maximumlikelihood decoders.
Design of orthonormal and overcomplete wavelet transforms based on rational sampling factors
 In Proc. Fifth SPIE Conference on Wavelet Applications in Industrial Processing
, 2007
"... Most wavelet transforms used in practice are based on integer sampling factors. Wavelet transforms based on rational sampling factors offer in principle the potential for timescale signal representations having a finer frequency resolution. Previous work on rational wavelet transforms and filter ba ..."
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Cited by 5 (4 self)
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Most wavelet transforms used in practice are based on integer sampling factors. Wavelet transforms based on rational sampling factors offer in principle the potential for timescale signal representations having a finer frequency resolution. Previous work on rational wavelet transforms and filter banks includes filter design methods and frequency domain implementations. We present several specific examples of Daubechiestype filters for a discrete orthonormal rational wavelet transform (FIR filters having a maximum number of vanishing moments) obtained using Gröbner bases. We also present the design of overcomplete rational wavelet transforms (tight frames) with FIR filters obtained using polynomial matrix spectral factorization.
JOINT DYNAMIC RESOURCE ALLOCATION AND WAVEFORM ADAPTATION IN COGNITIVE RADIO NETWORKS
"... This paper discusses the issue of dynamic resource allocation (DRA) in the context of cognitive radio (CR) networks. We present a general framework adopting generalized transmitter and receiver signalexpansion functions, which allow us to join DRA with waveform adaptation, two procedures that are cu ..."
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Cited by 4 (1 self)
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This paper discusses the issue of dynamic resource allocation (DRA) in the context of cognitive radio (CR) networks. We present a general framework adopting generalized transmitter and receiver signalexpansion functions, which allow us to join DRA with waveform adaptation, two procedures that are currently carried out separately. Moreover, the proposed DRA can handle many types of expansion functions or even combinations of different types of functions. An iterative game approach is adopted to perform multiplayer DRA, and the bestresponse strategies of players are derived and characterized using convex optimization. To reduce the implementation costs of having too many active expansion functions after optimization, we also propose to combine DRA with sparsity constraints for dynamic function selection. Generally, it incurs little rateperformance loss since the effective resources required by a CR are in fact sparse. Index Terms — cognitive radio, dynamic resource allocation, game theory, waveform adaptation, sparsity 1.
SemiSupervised Multiresolution Classification Using Adaptive Graph Filtering with Application to Indirect Bridge Structural Health Monitoring
"... We present a multiresolution classification framework with semisupervised learning on graphs with application to the indirect bridge structural health monitoring. Classification in realworld applications faces two main challenges: reliable features can be hard to extract and few labeled signals a ..."
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Cited by 4 (3 self)
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We present a multiresolution classification framework with semisupervised learning on graphs with application to the indirect bridge structural health monitoring. Classification in realworld applications faces two main challenges: reliable features can be hard to extract and few labeled signals are available for training. We propose a novel classification framework to address these problems: we use a multiresolution framework to deal with nonstationarities in the signals and extract features in each localized timefrequency region and semisupervised learning to train on both labeled and unlabeled signals. We further propose an adaptive graph filter for semisupervised classification that allows for classifying unlabeled as well as unseen signals and for correcting mislabeled signals. We validate the proposed framework on indirect bridge structural health monitoring and show that it performs significantly better than previous approaches.
Optimal placement of bearingonly sensors for target localization
 in Proc. of 2012 American Control Conference, 2012
"... Abstract—We investigate optimal placements of multiple bearingonly sensors for target localization in both 2D and 3D spaces. The target is assumed to be static, and sensortarget ranges are arbitrary but fixed. The Fisher information matrix is used to characterize the localization uncertainty. By e ..."
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Abstract—We investigate optimal placements of multiple bearingonly sensors for target localization in both 2D and 3D spaces. The target is assumed to be static, and sensortarget ranges are arbitrary but fixed. The Fisher information matrix is used to characterize the localization uncertainty. By employing frame theory, we show that there are two types of optimal sensor placements, regular and irregular. Necessary and sufficient conditions of optimal placements are presented. It is proved that an irregular optimal placement can be converted to a regular one in a lower dimensional space. We furthermore propose explicit algorithms to construct some important specific regular optimal placements. I.
Texture characterization of CT images based on ridgelet transform
 ICGST International Journal on Graphics, Vision and Image Processing
, 2009
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