Belhassen Bayar

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Non-negative matrix factorization (NMF) has proven to be a useful decomposition technique for multivariate data, where the non-negativity constraint is necessary to have a meaningful physical interpretation. NMF reduces the dimensionality of non-negative data by decomposing it into two smaller non-negative factors with physical interpretation for class(More)
Compressive sensing is the theory of sparse signal recovery from undersampled measurements or observations. Exact signal reconstruction is an NP hard problem. A convex approximation using the l<sub>1</sub>-norm has received a great deal of theoretical attention. Exact recovery using the l<sub>1</sub> approximation is only possible under strict conditions on(More)
When creating a forgery, a forger can modify an image using many different image editing operations. Since a forensic examiner must test for each of these, significant interest has arisen in the development of universal forensic algorithms capable of detecting many different image editing operations and manipulations. In this paper, we propose a universal(More)
Non-negative matrix factorization (NMF) has proven to be a useful decomposition for multivariate data. Specifically, NMF appears to have advantages over other clustering methods, such as hierarchical clustering, for identification of distinct molecular patterns in gene expression profiles. The NMF algorithm, however, is deterministic. In particular, it does(More)
—We consider a high dimension low sample-size mul-tivariate regression problem that accounts for correlation of the response variables. The system is under-determined as there are more parameters than samples. We show that the maximum likelihood approach with covariance estimation is senseless because the likelihood diverges. We subsequently propose a(More)
Articles [1] H. Abdul-Rahman and N. Chernov. Fast and numerically stable circle fit.tic non-negative matrix factorization: Theory and application to microar-ray data analysis. [6] C. Fischbacher and G. Stolz. The infinite XXZ quantum spin chain revisited: structure of low lying spectral bands and gaps.
The major challenge in reverse-engineering genetic regulatory networks is the small number of (time) measurements or experiments compared to the number of genes, which makes the system under-determined and hence unidentifiable. The only way to overcome the identifiability problem is to incorporate prior knowledge about the system. It is often assumed that(More)
Interpolating full-resolution color images from color-filter-array (CFA) samples is Image demosaicing. Bayer pattern is popular among various CFA patterns and demosaicing with this Bayer pattern produces high resolution color images. This paper presents a new demosaicing approach for spatially sampled image data perceived through a color filter array, and(More)
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