Dictionary design for distributed compressive sensing

Conventional dictionary learning frameworks attempt to find a set of atoms that promote both signal representation and signal sparsity for a class of signals. In distributed compressive sensing (DCS), in addition to intra-signal correlation, inter-signal correlation is also exploited in the joint signal reconstruction, which goes beyond the aim of the conventional dictionary learning framework. In this letter, we propose a new dictionary learning framework in order to improve signal reconstruction performance in DCS applications. By capitalizing on the sparse common component and innovations (SCCI) model [1], which captures both intra- and inter-signal correlation, the proposed method iteratively finds a dictionary design that promotes various goals: i) signal representation; ii) intra-signal correlation; and iii) inter-signal correlation. Simulation results show that our dictionary design leads to an improved DCS reconstruction performance in comparison to other designs.This work is supported by EPSRC Research Grant EP/K033700/1 and EP/K033166/1, the Fundamental Research Funds for the Central Universities (No. 2014JBM149), the State Key Laboratory of Rail Traffic Control and Safety (RCS2012ZT014) of Beijing Jiaotong University, the Natural Science Foundation of China (U1334202), the Key Grant Project of Chinese Ministry of Education (313006).This is the published manuscript. It is freely available online from the IEEE website here: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6880772. © 2014 IEE

Dictionary Learning for Blind One Bit Compressed Sensing

This letter proposes a dictionary learning algorithm for blind one bit compressed sensing. In the blind one bit compressed sensing framework, the original signal to be reconstructed from one bit linear random measurements is sparse in an unknown domain. In this context, the multiplication of measurement matrix \Ab and sparse domain matrix $\Phi$, \ie \Db=\Ab\Phi, should be learned. Hence, we use dictionary learning to train this matrix. Towards that end, an appropriate continuous convex cost function is suggested for one bit compressed sensing and a simple steepest-descent method is exploited to learn the rows of the matrix \Db. Experimental results show the effectiveness of the proposed algorithm against the case of no dictionary learning, specially with increasing the number of training signals and the number of sign measurements.Comment: 5 pages, 3 figure

Multi-modal dictionary learning for image separation with application in art investigation

In support of art investigation, we propose a new source separation method that unmixes a single X-ray scan acquired from double-sided paintings. In this problem, the X-ray signals to be separated have similar morphological characteristics, which brings previous source separation methods to their limits. Our solution is to use photographs taken from the front and back-side of the panel to drive the separation process. The crux of our approach relies on the coupling of the two imaging modalities (photographs and X-rays) using a novel coupled dictionary learning framework able to capture both common and disparate features across the modalities using parsimonious representations; the common component models features shared by the multi-modal images, whereas the innovation component captures modality-specific information. As such, our model enables the formulation of appropriately regularized convex optimization procedures that lead to the accurate separation of the X-rays. Our dictionary learning framework can be tailored both to a single- and a multi-scale framework, with the latter leading to a significant performance improvement. Moreover, to improve further on the visual quality of the separated images, we propose to train coupled dictionaries that ignore certain parts of the painting corresponding to craquelure. Experimentation on synthetic and real data - taken from digital acquisition of the Ghent Altarpiece (1432) - confirms the superiority of our method against the state-of-the-art morphological component analysis technique that uses either fixed or trained dictionaries to perform image separation.Comment: submitted to IEEE Transactions on Images Processin