Robust Rotation Synchronization via Low-rank and Sparse Matrix Decomposition

This paper deals with the rotation synchronization problem, which arises in global registration of 3D point-sets and in structure from motion. The problem is formulated in an unprecedented way as a "low-rank and sparse" matrix decomposition that handles both outliers and missing data. A minimization strategy, dubbed R-GoDec, is also proposed and evaluated experimentally against state-of-the-art algorithms on simulated and real data. The results show that R-GoDec is the fastest among the robust algorithms.Comment: The material contained in this paper is part of a manuscript submitted to CVI

Exploiting hidden block sparsity: Interdependent matching pursuit for cyclic feature detection

In this paper, we propose a novel Compressive Sensing (CS)-enhanced spectrum sensing approach for Cognitive Radio (CR) systems. The new framework enables cyclic feature detection with a significantly reduced sampling rate. We associate the new framework with a novel model-based greedy reconstruction algorithm: interdependent matching pursuit (IMP). For IMP, the hidden block sparsity owing to the symmetry present in the cyclic spectrum is exploited which effectively reduces the degree of freedom of problem. Compared with conventional CS with independent support selection, a remarkable spectrum reconstruction improvement is achieved by IMP.The work of Wei Chen is supported by the State Key Laboratory of Rail Traffic Control and Safety (No. RCS2012ZT014), Beijing Jiaotong University, and the Key grant Project of Chinese Ministry of Education (No.313006).This is the author accepted manuscript. The final version is available from IEEE via http://dx.doi.org/10.1109/GLOCOM.2013.683122

Sparse time-frequency decomposition based on dictionary adaptation

In this paper, we propose a time-frequency analysis method to obtain instantaneous frequencies and the corresponding decomposition by solving an optimization problem. In this optimization problem, the basis that is used to decompose the signal is not known a priori. Instead, it is adapted to the signal and is determined as part of the optimization problem. In this sense, this optimization problem can be seen as a dictionary adaptation problem, in which the dictionary is adaptive to one signal rather than a training set in dictionary learning. This dictionary adaptation problem is solved by using the augmented Lagrangian multiplier (ALM) method iteratively. We further accelerate the ALM method in each iteration by using the fast wavelet transform. We apply our method to decompose several signals, including signals with poor scale separation, signals with outliers and polluted by noise and a real signal. The results show that this method can give accurate recovery of both the instantaneous frequencies and the intrinsic mode functions

M/EEG source reconstruction based on Gabor thresholding in the source space

International audienceThanks to their high temporal resolution, source reconstruction based on Magnetoencephalography (MEG) and/or Electroencephalography (EEG) is an important tool for noninvasive functional brain imaging. Since the MEG/EEG inverse problem is ill-posed, inverse solvers employ priors on the sources. While priors are generally applied in the time domain, the time-frequency (TF) characteristics of brain signals are rarely employed as a spatio-temporal prior. In this work, we present an inverse solver which employs a structured sparse prior formed by the sum of $\ell_{21}$ and $\ell_{1}$ norms on the coefficients of the Gabor TF decomposition of the source activations. The resulting convex optimization problem is solved using a first-order scheme based on proximal operators. We provide empirical evidence based on EEG simulations that the proposed method is able to recover neural activations that are spatially sparse, temporally smooth and non-stationary. We compare our approach to alternative solvers based also on convex sparse priors, and demonstrate the benefit of promoting sparse Gabor decompositions via a mathematically principled iterative thresholding procedure