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Compressive sensing (CS) is mainly concerned with low-coherence pairs, since the number of samples needed to recover the signal is proportional to the mutual coherence between projection matrix and sparsifying matrix. Until now, papers on CS always assume the projection matrix to be a random matrix. In this paper, aiming at minimizing the mutual coherence, a method is proposed to optimize the projection matrix. This method is based on equiangular tight frame (ETF) design because an ETF has minimum coherence. It is impossible to solve the problem exactly because of the complexity. Therefore, an alternating minimization type method is used to find a feasible solution. The optimally designed projection matrix can further reduce the necessary number of samples for recovery or improve the recovery accuracy. The proposed method demonstrates better performance than conventional optimization methods, which brings benefits to both basis pursuit and orthogonal matching pursuit.

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MRSI has shown potential in the diagnosis and prognosis of glioblastoma multiforme (GBM) brain tumors, but its use is limited by difficult data interpretation. When the analyzed MRSI data present more than two tissue patterns, conventional non-negative matrix factorization (NMF) implementation may lead to a non-robust estimation. The aim of this article is to introduce an effective approach for the differentiation of GBM tissue patterns using MRSI data. A hierarchical non-negative matrix factorization (hNMF) method that can blindly separate the most important spectral sources in short-TE ¹H MRSI data is proposed. This algorithm consists of several levels of NMF, where only two tissue patterns are computed at each level. The method is demonstrated on both simulated and in vivo short-TE ¹H MRSI data in patients with GBM. For the in vivo study, the accuracy of the recovered spectral sources was validated using expert knowledge. Results show that hNMF is able to accurately estimate the three tissue patterns present in the tumoral and peritumoral area of a GBM, i.e. normal, tumor and necrosis, thus providing additional useful information that can help in the diagnosis of GBM. Moreover, the hNMF results can be displayed as easily interpretable maps showing the contribution of each tissue pattern to each voxel.

Abstract:In recent years, sparse representation-based techniques have shown great potential for pattern recognition problems. In this paper, the problem of polarimetric synthetic aperture radar (PolSAR) image classification is investigated using sparse representation-based classifiers (SRCs). We propose to take advantage of both polarimetric information and contextual information by combining sparsity-based classification methods with the concept of superpixels. Based on polarimetric feature vectors constructed by stacking a variety of polarimetric signatures and a superpixel map, two strategies are considered to perform polarimetric-contextual classification of PolSAR images. The first strategy starts by classifying the PolSAR image with pixel-wise SRC. Then, spatial regularization is imposed on the pixel-wise classification map by using majority voting within superpixels. In the second strategy, the PolSAR image is classified by taking superpixels as processing elements. The joint sparse representation-based classifier (JSRC) is employed to combine the polarimetric information contained in feature vectors and the contextual information provided by superpixels. Experimental results on real PolSAR datasets demonstrate the feasibility of the proposed approaches. It is proven that the classification performance is improved by using contextual information. A comparison with several other approaches also verifies the effectiveness of the proposed approach.