Sparse Base Constructed by the Non-negative Matrix Factorization

When the signal is sparse or compressible in a transform domain, the measurement matrix which is noncoherent with the transform matrix can be used to project transform coefficients to the low-dimensional vector, and this projection can maintain the information for signal reconstruction. The compressed sensing technology can achieve the reconstruction with high accuracy or high probability using small number of projection data. The signal’s reconstruction ability largely depends on its sparsity, as well as the non-coherence between the sampling matrix and the transform matrix. This paper proposes to use the NMF (non-negative matrix factorization) method to carry out sparse changes for the original signal and construct sparse transform base matrix φ. Besides, a comparative study between it and the transform matrix constructed by DFT (Discrete Fourier Transform) and DWT (Discrete Wavelet Transform) is conducted to measure the coherence degree and sparsity. Then the OMP (orthogonal matching pursuit) is adopted to analyze the signal’s restoration ability, showing that the restoration ability of NMF is superior to that of DFT and DWT.