Active Range Imaging via Random Gating

 

Authors: G. Tsagkatakis, A. Woiselle, G. Tzagkarakis, M. Bousquet, J.-L. Starck and P. Tsakalides
Journal: SPIE
Year: 2012
Download: SPIE


Abstract

Range Imaging (RI) has sparked an enthusiastic interest recently due to the numerous applications that can benefit from the presence 3D data. One of the most successful techniques for RI employs Time-of-Flight (ToF) cameras which emit and subsequently record laser pulses in order to estimate the distance between the camera and an object. A limitation of this class of RI is the requirement for a large number of frames that have to be captured in order to generate high resolution depth maps. In this work, we propose a novel approach for ToF based RI that utilizes the recently proposed framework of Compressed Sensing to dramatically reduce the number of necessary frames. Our technique employs a random gating function along with state-of-the-art minimization techniques in order to estimate the location of a returning laser pulse and infer the distance. To validate the theoretical motivation, software simulations were carried out. Our simulated results have shown that reconstruction of a depth map is possible from as low as 10% of the frames that traditional ToF cameras require with minimum reconstruction error while 20% sampling rates can achieve almost perfect reconstruction in low resolution regimes. Our experimental results have also shown that the proposed method is robust to various types of noise and applicable to realistic signal models. © (2012) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.

Compressive video classification in a low-dimensional manifold with learned distance metric

 

Authors: G. Tzagkarakis, G. Tsagkatakis, J.-L. Starck, P. Tsakalides
Journal: EUSIPCO
Year: 2012
Download: IEEE


Abstract

In this paper, we introduce an architecture for addressing the problem of video classification based on a set of compressed features, without the need of accessing the original full-resolution video data. In particular, the video frames are acquired directly in a compressed domain by means of random projections associated with a set of compressive measurements. This initial dimensionality reduction step is followed by distance metric learning for the construction of an informative distance matrix, which is then embedded in a manifold learning approach to increase the discriminative power of the random measurements in a lower-dimensional space. Classification results using a set of activity videos suggest that the proposed approach can be used effectively in cases when the acquisition and processing of full-resolution video data is characterized by increased consumption of the available power, memory and bandwidth, which may impede the operation of systems with limited resources.

Compressive video classification for decision systems with limited resources

 

Authors: G. Tzagkarakis, P. Charalampidis, G. Tsagkatakis, J.-L. Starck, P. Tsakalides
Journal: PCS
Year: 2012
Download: IEEE


Abstract

In this paper, we address the problem of video classification from a set of compressed features. In particular, the properties of linear random projections in the framework of compressive sensing are exploited to reduce the task of classifying a given video sequence into a problem of sparse reconstruction, based on feature vectors consisting of measurements lying in a low-dimensional compressed domain. This can be of great importance in decision systems with limited power, processing, and bandwidth resources, since the classification is performed without handling the original high-resolution video data, but working directly with the set of compressed measurements. The experimental evaluation verifies the efficiency of the proposed scheme and illustrates that the compressed measurements in conjunction with an appropriate decision rule result in an effective video classification scheme, which meets the constraints of systems with limited resources.

Spherical 3D Isotropic Wavelets

 

Authors: F. Lanusse, A. Rassat, J.-L. Starck
Journal: A&A
Year: 2012
Download: ADS | arXiv


Abstract

Future cosmological surveys will provide 3D large scale structure maps with large sky coverage, for which a 3D Spherical Fourier-Bessel (SFB) analysis in spherical coordinates is natural. Wavelets are particularly well-suited to the analysis and denoising of cosmological data, but a spherical 3D isotropic wavelet transform does not currently exist to analyse spherical 3D data. The aim of this paper is to present a new formalism for a spherical 3D isotropic wavelet, i.e. one based on the SFB decomposition of a 3D field and accompany the formalism with a public code to perform wavelet transforms. We describe a new 3D isotropic spherical wavelet decomposition based on the undecimated wavelet transform (UWT) described in Starck et al. 2006. We also present a new fast Discrete Spherical Fourier-Bessel Transform (DSFBT) based on both a discrete Bessel Transform and the HEALPIX angular pixelisation scheme. We test the 3D wavelet transform and as a toy-application, apply a denoising algorithm in wavelet space to the Virgo large box cosmological simulations and find we can successfully remove noise without much loss to the large scale structure. We have described a new spherical 3D isotropic wavelet transform, ideally suited to analyse and denoise future 3D spherical cosmological surveys, which uses a novel Discrete Spherical Fourier-Bessel Transform. We illustrate its potential use for denoising using a toy model. All the algorithms presented in this paper are available for download as a public code called MRS3D at this http URL.

Design of a Compressive Remote Imaging System Compensating a Highly Lightweight Encoding with a Refined Decoding Scheme

 

Authors: G. Tzagkarakis, A. Woiselle, P. Tsakalides, J.-L. Starck
Journal: VISAPP
Year: 2012
Download: Sitepress


Abstract

Lightweight remote imaging systems have been increasingly used in surveillance and reconnaissance. Nevertheless, the limited power, processing and bandwidth resources is a major issue for the existing solutions, not well addressed by the standard video compression techniques. On the one hand, the MPEGx family achieves a balance between the reconstruction quality and the required bit-rate by exploiting potential intra- and interframe redundancies at the encoder, but at the cost of increased memory and processing demands. On the other hand, the M-JPEG approach consists of a computationally efficient encoding process, with the drawback of resulting in much higher bit-rates. In this paper, we cope with the growing compression ratios, required for all remote imaging applications, by exploiting the inherent property of compressive sensing (CS), acting simultaneously as a sensing and compression framework. The proposed compressive video sensing (CVS) system incorporates the advantages of a v ery simple CS-based encoding process, while putting the main computational burden at the decoder combining the efficiency of a motion compensation procedure for the extraction of inter-frame correlations, along with an additional super-resolution step to enhance the quality of reconstructed frames. The experimental results reveal a significant improvement of the reconstruction quality when compared with M-JPEG, at equal or even lower bit-rates.

Sparse Solution of Underdetermined Systems of Linear Equations by Stagewise Orthogonal Matching Pursuit

 

Authors: D. L. Donoho, Y. Tsaig, I. Drori, J.-L. Starck
Journal: IEEE
Year: 2012
Download: IEEE


Abstract

Finding the sparsest solution to underdetermined systems of linear equations y = Φx is NP-hard in general. We show here that for systems with “typical”/“random” Φ, a good approximation to the sparsest solution is obtained by applying a fixed number of standard operations from linear algebra. Our proposal, Stagewise Orthogonal Matching Pursuit (StOMP), successively transforms the signal into a negligible residual. Starting with initial residual r0 = y, at the s -th stage it forms the “matched filter” ΦTrs-1, identifies all coordinates with amplitudes exceeding a specially chosen threshold, solves a least-squares problem using the selected coordinates, and subtracts the least-squares fit, producing a new residual. After a fixed number of stages (e.g., 10), it stops. In contrast to Orthogonal Matching Pursuit (OMP), many coefficients can enter the model at each stage in StOMP while only one enters per stage in OMP; and StOMP takes a fixed number of stages (e.g., 10), while OMP can take many (e.g., n). We give both theoretical and empirical support for the large-system effectiveness of StOMP. We give numerical examples showing that StOMP rapidly and reliably finds sparse solutions in compressed sensing, decoding of error-correcting codes, and overcomplete representation.

Indoor positioning in Wireless LANS using compressive sensing signal-strength fingerprints

 

Authors: D. Milioris, G. Tzagkarakis, P. Jacquet
Journal: EUSIPCO
Year: 2011
Download: IEEE


Abstract

Accurate indoor localization is a significant task for many ubiquitous and pervasive computing applications, with numerous solutions based on IEEE802.11, Bluetooth, ultrasound and infrared technologies being proposed. The inherent sparsity present in the problem of location estimation motivates in a natural fashion the use of the recently introduced theory of compressive sensing (CS), which states that a signal having a sparse representation in an appropriate basis can be reconstructed with high accuracy from a small number of random linear projections. In the present work, we exploit the framework of CS to perform accurate indoor localization based on signal-strength measurements, while reducing significantly the amount of information transmitted from a wireless device with limited power, storage, and processing capabilities to a central server. Equally importantly, the inherent property of CS acting as a weak encryption process is demonstrated by showing that the proposed approach presents an increased robustness to potential intrusions of an unauthorized entity. The experimental evaluation reveals that the proposed CS-based localization technique is superior in terms of an increased localization accuracy in conjunction with a low computational complexity when compared with previous statistical fingerprint-based methods.

Joint Sparse Signal Ensemble Reconstruction in a WSN Using Decentralized Bayesian Matching Pursuit

 

Authors: G. Tzagkarakis, J.-L. Starck, P. Tsakalides
Journal: EUSIPCO
Year: 2011
Download: IEEE


Abstract

Wireless networks comprised of low-cost sensory devices have been increasingly used in surveillance both at the civilian and military levels. Limited power, processing, and bandwidth resources is a major issue for abandoned sensors, which should be addressed to increase the network's performance and lifetime. In this work, the framework of compressive sensing is exploited, which allows accurate recovery of signals being sparse in some basis using only a small number of random incoherent projections. In particular, a recently introduced Bayesian Matching Pursuit method is modified in a decentralized way to reconstruct a multi-signal ensemble acquired by the nodes of a wireless sensor network, by exploiting a joint sparsity structure among the signals of the ensemble. The proposed approach requires a minimal amount of data transmissions among the sensors and a central node thus preserving the sensors' limited resources. At the same time, it achieves a reconstruction performance comparable to other distributed compressive sensing methods, which require the communication of a whole set of measurements to the central node.

Feasibility and performances of compressed-sensing and sparse map-making with Herschel/PACS data

 

Authors: N. Barbey, M. Sauvage, J.-L. Starck, R. Ottensamer, P. Chanial
Journal: A&A
Year: 2011
Download: ADS | arXiv


Abstract

The Herschel Space Observatory of ESA was launched in May 2009 and is in operation since. From its distant orbit around L2 it needs to transmit a huge quantity of information through a very limited bandwidth. This is especially true for the PACS imaging camera which needs to compress its data far more than what can be achieved with lossless compression. This is currently solved by including lossy averaging and rounding steps on board. Recently, a new theory called compressed-sensing emerged from the statistics community. This theory makes use of the sparsity of natural (or astrophysical) images to optimize the acquisition scheme of the data needed to estimate those images. Thus, it can lead to high compression factors.
A previous article by Bobin et al. (2008) showed how the new theory could be applied to simulated Herschel/PACS data to solve the compression requirement of the instrument. In this article, we show that compressed-sensing theory can indeed be successfully applied to actual Herschel/PACS data and give significant improvements over the standard pipeline. In order to fully use the redundancy present in the data, we perform full sky map estimation and decompression at the same time, which cannot be done in most other compression methods. We also demonstrate that the various artifacts affecting the data (pink noise, glitches, whose behavior is a priori not well compatible with compressed-sensing) can be handled as well in this new framework. Finally, we make a comparison between the methods from the compressed-sensing scheme and data acquired with the standard compression scheme. We discuss improvements that can be made on ground for the creation of sky maps from the data.

3-D Data Denoising and Inpainting with the Low-Redundancy Fast Curvelet Transform

 

Authors: A. Woiselle, J.-L. Starck, J. Fadili
Journal: Journal of Mathematical Imaging and Vision
Year: 2010
Download: Springer


Abstract

In this paper, we first present a new implementation of the 3-D fast curvelet transform, which is nearly 2.5 less redundant than the Curvelab (wrapping-based) implementation as originally proposed in Ying et al. (Proceedings of wavelets XI conference, San Diego, 2005) and Candès et al. (SIAM Multiscale Model. Simul. 5(3):861–899, 2006), which makes it more suitable to applications including massive data sets. We report an extensive comparison in denoising with the Curvelab implementation as well as other 3-D multi-scale transforms with and without directional selectivity. The proposed implementation proves to be a very good compromise between redundancy, rapidity and performance. Secondly, we exemplify its usefulness on a variety of applications including denoising, inpainting, video de-interlacing and sparse component separation. The obtained results are good with very simple algorithms and virtually no parameter to tune.