Constrained Restoration and the Recovery of Discontinuities
IEEE Transactions on Pattern Analysis and Machine Intelligence
Sparse Image Coding Using a 3D Non-Negative Tensor Factorization
ICCV '05 Proceedings of the Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1 - Volume 01
Non-negative tensor factorization with applications to statistics and computer vision
ICML '05 Proceedings of the 22nd international conference on Machine learning
Algorithm 862: MATLAB tensor classes for fast algorithm prototyping
ACM Transactions on Mathematical Software (TOMS)
A Generalized Divergence Measure for Nonnegative Matrix Factorization
Neural Computation
Novel Multi-layer Non-negative Tensor Factorization with Sparsity Constraints
ICANNGA '07 Proceedings of the 8th international conference on Adaptive and Natural Computing Algorithms, Part II
Blind Image Separation Using Nonnegative Matrix Factorization with Gibbs Smoothing
Neural Information Processing
Csiszár’s divergences for non-negative matrix factorization: family of new algorithms
ICA'06 Proceedings of the 6th international conference on Independent Component Analysis and Blind Signal Separation
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Nonnegative Tensor Factorization (NTF) is an emerging technique in multidimensional signal analysis and it can be used to find parts-based representations of high-dimensional data. In many applications such as multichannel spectrogram processing or multiarray spectra analysis, the unknown features have locally smooth temporal or spatial structure. In this paper, we incorporate to an objective function in NTF additional smoothness constrains that considerably improve the unknown features. In our approach, we propose to use the Markov Random Field (MRF) model that is commonly-used in tomographic image reconstruction to model local smoothness properties of 2D reconstructed images. We extend this model to multidimensional case whereby smoothness can be enforced in all dimensions of a multi-dimensional array. We analyze different clique energy functions that are a subject to MRF. Some numerical results performed on a multidimensional image dataset are presented.