A Matrix-Based Two-Dimensional Regularization Algorithm for Signal-to-Noise Ratio Enhancement of Multidimensional Spectral Data

We present a new spectral image processing algorithm, the “matrix maximum entropy method” (MxMEM), which offers efficient signal-to-noise ratio (SNR) enhancement of multidimensional spectral data. MxMEM is based upon two previous regularization methods that employ the maximum entropy concept. The first is a one-dimensional (1D) algorithm, which smoothes individual vectors, called the two-point maximum entropy method (TPMEM). The second is a two-dimensional (2D) form called 2D TPMEM, that smoothes images but processes them one vector at a time. MxMEM is a truly two dimensional image processing algorithm in that its “smoothing engine” performs two-dimensional processing in every iteration. We demonstrate that this matrix-based construction makes more effective use of two-dimensionally embedded information and thus confers significant advantages over other regularization approaches. In addition, we utilize the concept that individual related Raman spectra can be combined in a matrix to form an artificial Raman “image”. We show that, when processed as an image, superior SNR enhancement is achieved compared to processing the same data by TPMEM one spectrum at a time.