arXiv subjects

Pascal Frossard

Publications and source records attributed to Pascal Frossard.

216 records · Page 12Linked to original sources

arXiv2012

Learning Smooth Pattern Transformation Manifolds

Manifold models provide low-dimensional representations that are useful for processing and analyzing data in a transformation-invariant way. In this paper, we study the problem of learning smooth pattern transformation manifolds from image sets that represent observations of geometrically transformed signals. In order to construct a manifold, we build a representative pattern whose transformations accurately fit various input images. We examine two objectives of the manifold building problem, namely, approximation and classification. For the approximation problem, we propose a greedy method that constructs a representative pattern by selecting analytic atoms from a continuous dictionary manifold. We present a DC (Difference-of-Convex) optimization scheme that is applicable to a wide range of transformation and dictionary models, and demonstrate its application to transformation manifolds generated by rotation, translation and anisotropic scaling of a reference pattern. Then, we generalize this approach to a setting with multiple transformation manifolds, where each manifold represents a different class of signals. We present an iterative multiple manifold building algorithm such that the classification accuracy is promoted in the learning of the representative patterns. Experimental results suggest that the proposed methods yield high accuracy in the approximation and classification of data compared to some reference methods, while the invariance to geometric transformations is achieved due to the transformation manifold model.

cs.CV↗

arXiv2012

Joint Reconstruction of Multi-view Compressed Images

The distributed representation of correlated multi-view images is an important problem that arise in vision sensor networks. This paper concentrates on the joint reconstruction problem where the distributively compressed correlated images are jointly decoded in order to improve the reconstruction quality of all the compressed images. We consider a scenario where the images captured at different viewpoints are encoded independently using common coding solutions (e.g., JPEG, H.264 intra) with a balanced rate distribution among different cameras. A central decoder first estimates the underlying correlation model from the independently compressed images which will be used for the joint signal recovery. The joint reconstruction is then cast as a constrained convex optimization problem that reconstructs total-variation (TV) smooth images that comply with the estimated correlation model. At the same time, we add constraints that force the reconstructed images to be consistent with their compressed versions. We show by experiments that the proposed joint reconstruction scheme outperforms independent reconstruction in terms of image quality, for a given target bit rate. In addition, the decoding performance of our proposed algorithm compares advantageously to state-of-the-art distributed coding schemes based on disparity learning and on the DISCOVER.

cs.MM↗

arXiv2012

Markov Decision Process Based Energy-Efficient On-Line Scheduling for Slice-Parallel Video Decoders on Multicore Systems

We consider the problem of energy-efficient on-line scheduling for slice-parallel video decoders on multicore systems. We assume that each of the processors are Dynamic Voltage Frequency Scaling (DVFS) enabled such that they can independently trade off performance for power, while taking the video decoding workload into account. In the past, scheduling and DVFS policies in multi-core systems have been formulated heuristically due to the inherent complexity of the on-line multicore scheduling problem. The key contribution of this report is that we rigorously formulate the problem as a Markov decision process (MDP), which simultaneously takes into account the on-line scheduling and per-core DVFS capabilities; the power consumption of the processor cores and caches; and the loss tolerant and dynamic nature of the video decoder's traffic. In particular, we model the video traffic using a Direct Acyclic Graph (DAG) to capture the precedence constraints among frames in a Group of Pictures (GOP) structure, while also accounting for the fact that frames have different display/decoding deadlines and non-deterministic decoding complexities. The objective of the MDP is to minimize long-term power consumption subject to a minimum Quality of Service (QoS) constraint related to the decoder's throughput. Although MDPs notoriously suffer from the curse of dimensionality, we show that, with appropriate simplifications and approximations, the complexity of the MDP can be mitigated. We implement a slice-parallel version of H.264 on a multiprocessor ARM (MPARM) virtual platform simulator, which provides cycle-accurate and bus signal-accurate simulation for different processors. We use this platform to generate realistic video decoding traces with which we evaluate the proposed on-line scheduling algorithm in Matlab.

cs.MM↗

arXiv2012

Thresholding-based reconstruction of compressed correlated signals

We consider the problem of recovering a set of correlated signals (e.g., images from different viewpoints) from a few linear measurements per signal. We assume that each sensor in a network acquires a compressed signal in the form of linear measurements and sends it to a joint decoder for reconstruction. We propose a novel joint reconstruction algorithm that exploits correlation among underlying signals. Our correlation model considers geometrical transformations between the supports of the different signals. The proposed joint decoder estimates the correlation and reconstructs the signals using a simple thresholding algorithm. We give both theoretical and experimental evidence to show that our method largely outperforms independent decoding in terms of support recovery and reconstruction quality.

cs.NI↗

arXiv2012

Progressive quantization in distributed average consensus

We consider the problem of distributed average consensus in a sensor network where sensors exchange quantized information with their neighbors. We propose a novel quantization scheme that exploits the increasing correlation between the values exchanged by the sensors throughout the iterations of the consensus algorithm. A low complexity, uniform quantizer is implemented in each sensor, and refined quantization is achieved by progressively reducing the quantization intervals during the convergence of the consensus algorithm. We propose a recurrence relation for computing the quantization parameters that depend on the network topology and the communication rate. We further show that the recurrence relation can lead to a simple exponential model for the size of the quantization step size over the iterations, whose parameters can be computed a priori. Finally, simulation results demonstrate the effectiveness of the progressive quantization scheme that leads to the consensus solution even at low communication rate.

cs.DC↗

arXiv2012

Interactive multiview video system with non-complex navigation at the decoder

Multiview video with interactive and smooth view switching at the receiver is a challenging application with several issues in terms of effective use of storage and bandwidth resources, reactivity of the system, quality of the viewing experience and system complexity. The classical decoding system for generating virtual views first projects a reference or encoded frame to a given viewpoint and then fills in the holes due to potential occlusions. This last step still constitutes a complex operation with specific software or hardware at the receiver and requires a certain quantity of information from the neighboring frames for insuring consistency between the virtual images. In this work we propose a new approach that shifts most of the burden due to interactivity from the decoder to the encoder, by anticipating the navigation of the decoder and sending auxiliary information that guarantees temporal and interview consistency. This leads to an additional cost in terms of transmission rate and storage, which we minimize by using optimization techniques based on the user behavior modeling. We show by experiments that the proposed system represents a valid solution for interactive multiview systems with classical decoders.

cs.MM↗

arXiv2011

Discretization of Parametrizable Signal Manifolds

Transformation-invariant analysis of signals often requires the computation of the distance from a test pattern to a transformation manifold. In particular, the estimation of the distances between a transformed query signal and several transformation manifolds representing different classes provides essential information for the classification of the signal. In many applications the computation of the exact distance to the manifold is costly, whereas an efficient practical solution is the approximation of the manifold distance with the aid of a manifold grid. In this paper, we consider a setting with transformation manifolds of known parameterization. We first present an algorithm for the selection of samples from a single manifold that permits to minimize the average error in the manifold distance estimation. Then we propose a method for the joint discretization of multiple manifolds that represent different signal classes, where we optimize the transformation-invariant classification accuracy yielded by the discrete manifold representation. Experimental results show that sampling each manifold individually by minimizing the manifold distance estimation error outperforms baseline sampling solutions with respect to registration and classification accuracy. Performing an additional joint optimization on all samples improves the classification performance further. Moreover, given a fixed total number of samples to be selected from all manifolds, an asymmetric distribution of samples to different manifolds depending on their geometric structures may also increase the classification accuracy in comparison with the equal distribution of samples.

cs.CV↗

arXiv2011

Distributed sensor failure detection in sensor networks

We investigate the problem of distributed sensors' failure detection in networks with a small number of defective sensors, whose measurements differ significantly from neighboring sensor measurements. Defective sensors are represented by non-zero values in binary sparse signals. We build on the sparse nature of the binary sensor failure signals and propose a new distributed detection algorithm based on Group Testing (GT). The distributed GT algorithm estimates the set of defective sensors from a small number of linearly independent binary messages exchanged by the sensors. The distributed GT algorithm uses a low complexity distance decoder that is robust to noisy messages. We first consider networks with only one defective sensor and determine the minimal number of linearly independent messages needed for detection of the defective sensor with high probability. We then extend our study to the detection of multiple defective sensors by modifying appropriately the message exchange protocol and the decoding procedure. We show through experimentation that, for small and medium sized networks, the number of messages required for successful detection is actually smaller than the minimal number computed in the analysis. Simulations demonstrate that the proposed method outperforms methods based on random walk measurements collection in terms of detection performance and convergence rate. Finally, the proposed method is resilient to network dynamics due to the effective gossip-based message dissemination protocol.

cs.NI↗

arXiv2011

Approximate Decoding Approaches for Network Coded Correlated Data

This paper considers a framework where data from correlated sources are transmitted with help of network coding in ad-hoc network topologies. The correlated data are encoded independently at sensors and network coding is employed in the intermediate nodes in order to improve the data delivery performance. In such settings, we focus on the problem of reconstructing the sources at decoder when perfect decoding is not possible due to losses or bandwidth bottlenecks. We first show that the source data similarity can be used at decoder to permit decoding based on a novel and simple approximate decoding scheme. We analyze the influence of the network coding parameters and in particular the size of finite coding fields on the decoding performance. We further determine the optimal field size that maximizes the expected decoding performance as a trade-off between information loss incurred by limiting the resolution of the source data and the error probability in the reconstructed data. Moreover, we show that the performance of the approximate decoding improves when the accuracy of the source model increases even with simple approximate decoding techniques. We provide illustrative examples about the possible of our algorithms that can be deployed in sensor networks and distributed imaging applications. In both cases, the experimental results confirm the validity of our analysis and demonstrate the benefits of our low complexity solution for delivery of correlated data sources.

cs.NI↗

arXiv2011

Correlation Estimation from Compressed Images

This paper addresses the problem of correlation estimation in sets of compressed images. We consider a framework where images are represented under the form of linear measurements due to low complexity sensing or security requirements. We assume that the images are correlated through the displacement of visual objects due to motion or viewpoint change and the correlation is effectively represented by optical flow or motion field models. The correlation is estimated in the compressed domain by jointly processing the linear measurements. We first show that the correlated images can be efficiently related using a linear operator. Using this linear relationship we then describe the dependencies between images in the compressed domain. We further cast a regularized optimization problem where the correlation is estimated in order to satisfy both data consistency and motion smoothness objectives with a Graph Cut algorithm. We analyze in detail the correlation estimation performance and quantify the penalty due to image compression. Extensive experiments in stereo and video imaging applications show that our novel solution stays competitive with methods that implement complex image reconstruction steps prior to correlation estimation. We finally use the estimated correlation in a novel joint image reconstruction scheme that is based on an optimization problem with sparsity priors on the reconstructed images. Additional experiments show that our correlation estimation algorithm leads to an effective reconstruction of pairs of images in distributed image coding schemes that outperform independent reconstruction algorithms by 2 to 4 dB.

cs.CV↗

arXiv2011

Correlation-aware Resource Allocation in Multi-Cell Networks

We propose a cross-layer strategy for resource allocation between spatially correlated sources in the uplink of multi-cell FDMA networks. Our objective is to find the optimum power and channel to sources, in order to minimize the maximum distortion achieved by any source in the network. Given that the network is multi-cell, the inter-cell interference must also be taken into consideration. This resource allocation problem is NP-hard and the optimal solution can only be found by exhaustive search over the entire solution space, which is not computationally feasible. We propose a three step method to be performed separately by the scheduler in each cell, which finds cross-layer resource allocation in simple steps. The three- step algorithm separates the problem into inter-cell resource management, grouping of sources for joint decoding, and intra- cell channel assignment. For each of the steps we propose allocation methods that satisfy different design constraints. In the simulations we compare methods for each step of the algorithm. We also demonstrate the overall gain of using correlation-aware resource allocation for a typical multi-cell network of Gaussian sources. We show that, while using correlation in compression and joint decoding can achieve 25% loss in distortion over independent decoding, this loss can be increased to 37% when correlation is also utilized in resource allocation method. This significant distortion loss motivates further work in correlation-aware resource allocation. Overall, we find that our method achieves a 60% decrease in 5 percentile distortion compared to independent methods.

cs.IT↗

arXiv2011

Distributed Representation of Geometrically Correlated Images with Compressed Linear Measurements

This paper addresses the problem of distributed coding of images whose correlation is driven by the motion of objects or positioning of the vision sensors. It concentrates on the problem where images are encoded with compressed linear measurements. We propose a geometry-based correlation model in order to describe the common information in pairs of images. We assume that the constitutive components of natural images can be captured by visual features that undergo local transformations (e.g., translation) in different images. We first identify prominent visual features by computing a sparse approximation of a reference image with a dictionary of geometric basis functions. We then pose a regularized optimization problem to estimate the corresponding features in correlated images given by quantized linear measurements. The estimated features have to comply with the compressed information and to represent consistent transformation between images. The correlation model is given by the relative geometric transformations between corresponding features. We then propose an efficient joint decoding algorithm that estimates the compressed images such that they stay consistent with both the quantized measurements and the correlation model. Experimental results show that the proposed algorithm effectively estimates the correlation between images in multi-view datasets. In addition, the proposed algorithm provides effective decoding performance that compares advantageously to independent coding solutions as well as state-of-the-art distributed coding schemes based on disparity learning.

cs.CV↗

arXiv2011

Clustering with Multi-Layer Graphs: A Spectral Perspective

Observational data usually comes with a multimodal nature, which means that it can be naturally represented by a multi-layer graph whose layers share the same set of vertices (users) with different edges (pairwise relationships). In this paper, we address the problem of combining different layers of the multi-layer graph for improved clustering of the vertices compared to using layers independently. We propose two novel methods, which are based on joint matrix factorization and graph regularization framework respectively, to efficiently combine the spectrum of the multiple graph layers, namely the eigenvectors of the graph Laplacian matrices. In each case, the resulting combination, which we call a "joint spectrum" of multiple graphs, is used for clustering the vertices. We evaluate our approaches by simulations with several real world social network datasets. Results demonstrate the superior or competitive performance of the proposed methods over state-of-the-art technique and common baseline methods, such as co-regularization and summation of information from individual graphs.

cs.LG↗

arXiv2011

Chebyshev Polynomial Approximation for Distributed Signal Processing

Unions of graph Fourier multipliers are an important class of linear operators for processing signals defined on graphs. We present a novel method to efficiently distribute the application of these operators to the high-dimensional signals collected by sensor networks. The proposed method features approximations of the graph Fourier multipliers by shifted Chebyshev polynomials, whose recurrence relations make them readily amenable to distributed computation. We demonstrate how the proposed method can be used in a distributed denoising task, and show that the communication requirements of the method scale gracefully with the size of the network.

cs.DC↗

arXiv2011

Selection of network coding nodes for minimal playback delay in streaming overlays

Network coding permits to deploy distributed packet delivery algorithms that locally adapt to the network availability in media streaming applications. However, it may also increase delay and computational complexity if it is not implemented efficiently. We address here the effective placement of nodes that implement randomized network coding in overlay networks, so that the goodput is kept high while the delay for decoding stays small in streaming applications. We first estimate the decoding delay at each client, which depends on the innovative rate in the network. This estimation permits to identify the nodes that have to perform coding for a reduced decoding delay. We then propose two iterative algorithms for selecting the nodes that should perform network coding. The first algorithm relies on the knowledge of the full network statistics. The second algorithm uses only local network statistics at each node. Simulation results show that large performance gains can be achieved with the selection of only a few network coding nodes. Moreover, the second algorithm performs very closely to the central estimation strategy, which demonstrates that the network coding nodes can be selected efficiently in a distributed manner. Our scheme shows large gains in terms of achieved throughput, delay and video quality in realistic overlay networks when compared to methods that employ traditional streaming strategies as well as random network nodes selection algorithms.

cs.MM↗

arXiv2009

A note on the data-driven capacity of P2P networks

We consider two capacity problems in P2P networks. In the first one, the nodes have an infinite amount of data to send and the goal is to optimally allocate their uplink bandwidths such that the demands of every peer in terms of receiving data rate are met. We solve this problem through a mapping from a node-weighted graph featuring two labels per node to a max flow problem on an edge-weighted bipartite graph. In the second problem under consideration, the resource allocation is driven by the availability of the data resource that the peers are interested in sharing. That is a node cannot allocate its uplink resources unless it has data to transmit first. The problem of uplink bandwidth allocation is then equivalent to constructing a set of directed trees in the overlay such that the number of nodes receiving the data is maximized while the uplink capacities of the peers are not exceeded. We show that the problem is NP-complete, and provide a linear programming decomposition decoupling it into a master problem and multiple slave subproblems that can be resolved in polynomial time. We also design a heuristic algorithm in order to compute a suboptimal solution in a reasonable time. This algorithm requires only a local knowledge from nodes, so it should support distributed implementations. We analyze both problems through a series of simulation experiments featuring different network sizes and network densities. On large networks, we compare our heuristic and its variants with a genetic algorithm and show that our heuristic computes the better resource allocation. On smaller networks, we contrast these performances to that of the exact algorithm and show that resource allocation fulfilling a large part of the peer can be found, even for hard configuration where no resources are in excess.

cs.DS↗

arXiv2009

Graph-based classification of multiple observation sets

We consider the problem of classification of an object given multiple observations that possibly include different transformations. The possible transformations of the object generally span a low-dimensional manifold in the original signal space. We propose to take advantage of this manifold structure for the effective classification of the object represented by the observation set. In particular, we design a low complexity solution that is able to exploit the properties of the data manifolds with a graph-based algorithm. Hence, we formulate the computation of the unknown label matrix as a smoothing process on the manifold under the constraint that all observations represent an object of one single class. It results into a discrete optimization problem, which can be solved by an efficient and low complexity algorithm. We demonstrate the performance of the proposed graph-based algorithm in the classification of sets of multiple images. Moreover, we show its high potential in video-based face recognition, where it outperforms state-of-the-art solutions that fall short of exploiting the manifold structure of the face image data sets.

cs.CV↗

arXiv2008

Polynomial Filtering for Fast Convergence in Distributed Consensus

In the past few years, the problem of distributed consensus has received a lot of attention, particularly in the framework of ad hoc sensor networks. Most methods proposed in the literature address the consensus averaging problem by distributed linear iterative algorithms, with asymptotic convergence of the consensus solution. The convergence rate of such distributed algorithms typically depends on the network topology and the weights given to the edges between neighboring sensors, as described by the network matrix. In this paper, we propose to accelerate the convergence rate for given network matrices by the use of polynomial filtering algorithms. The main idea of the proposed methodology is to apply a polynomial filter on the network matrix that will shape its spectrum in order to increase the convergence rate. Such an algorithm is equivalent to periodic updates in each of the sensors by aggregating a few of its previous estimates. We formulate the computation of the coefficients of the optimal polynomial as a semi-definite program that can be efficiently and globally solved for both static and dynamic network topologies. We finally provide simulation results that demonstrate the effectiveness of the proposed solutions in accelerating the convergence of distributed consensus averaging problems.

cs.IT↗