Blind Spectral Signal Deconvolution with Sparsity Regularization: An Iteratively Reweighted Least-Squares Solution

Spectral signals often suffer from the common problems of band overlap and random Gaussian noise. To address these problems, we propose a sparsity regularization-based model that deconvolutes the degraded spectral signals. Sparsity regularization is achieved by fitting the probability density function of the gradient of the signal, and then, the iteratively reweighted least-squares method is used to solve the minimization problem. Results from experiments using real spectral signals showed that this algorithm separates the overlapping peaks and effectively suppresses the noise. The deconvoluted spectral signals will promote the practical application of infrared spectral analysis in the fields of target recognition, material identification, and chemometrics analysis.

[1]  Houzhang Fang,et al.  Semi-Blind Spectral Deconvolution with Adaptive Tikhonov Regularization , 2012, Applied spectroscopy.

[2]  Douglas J. Moffatt,et al.  Fourier Self-Deconvolution: A Method for Resolving Intrinsically Overlapped Bands , 1981 .

[3]  VÍCTOR A. LÓRENZ-FONFRÍA,et al.  The Role and Selection of the Filter Function in Fourier Self-Deconvolution Revisited , 2009, Applied spectroscopy.

[4]  David D. Allred,et al.  Deconvolution of the Raman spectrum of amorphous carbon , 1995 .

[5]  Hai Liu,et al.  Parametric spectral signal restoration via maximum entropy constraint and its application , 2015, 2015 IEEE Signal Processing and Signal Processing Education Workshop (SP/SPE).

[6]  Hai Liu,et al.  Joint Baseline-Correction and Denoising for Raman Spectra , 2015, Applied spectroscopy.

[7]  Ling-Jian Meng,et al.  An inter-comparison of three spectral-deconvolution algorithms for gamma-ray spectroscopy , 1999 .

[8]  Frédo Durand,et al.  Image and depth from a conventional camera with a coded aperture , 2007, SIGGRAPH 2007.

[9]  P. Jansson.  Deconvolution of images and spectra , 1997 .

[10]  Tianxu Zhang,et al.  Blind spectrum reconstruction algorithm with L0-sparse representation , 2015 .

[11]  Sanya Liu,et al.  Spectral blind deconvolution with differential entropy regularization for infrared spectrum , 2015 .

[12]  K. Bouyoucef,et al.  Prior knowledge and multiscaling in statistical estimation of signal-to-noise ratio - Application to deconvolution regularization , 1995, Signal Process..

[13]  V. Lorenz-Fonfria,et al.  Maximum Entropy Deconvolution of Infrared Spectra: Use of a Novel Entropy Expression without Sign Restriction , 2005, Applied spectroscopy.

[14]  Ziqiang Hu,et al.  High-Order Statistical Blind Deconvolution of Spectroscopic Data with a Gauss—Newton Algorithm , 2006, Applied spectroscopy.

[15]  Marc Van Droogenbroeck.  Generalized iterative algorithm for spectral signal deconvolution , 1992 .

[16]  Ziqiang Hu,et al.  Constrained high-order statistical blind deconvolution of spectral data , 2005 .

[17]  A. J. Shaka,et al.  Postprocessing and sparse blind source separation of positive and partially overlapped data , 2011, Signal Process..

[18]  Hai Liu,et al.  A MAP-based algorithm for spectroscopic semi-blind deconvolution. , 2012, The Analyst.

[19]  Kenneth E. Barner,et al.  Iteratively re-weighted least squares for sparse signal reconstruction from noisy measurements , 2009, 2009 43rd Annual Conference on Information Sciences and Systems.

[20]  Zhuowen Tu,et al.  Robust $L_{2}E$ Estimation of Transformation for Non-Rigid Registration , 2015, IEEE Transactions on Signal Processing.

[21]  Esteve Padrós,et al.  Curve-fitting overlapped bands: quantification and improvement of curve-fitting robustness in the presence of errors in the model and in the data. , 2004, The Analyst.

[22]  ROHIT BHARGAVA,et al.  Infrared Spectroscopic Imaging: The Next Generation , 2012, Applied spectroscopy.

[23]  Erik Andries,et al.  Spectral Multivariate Calibration with Wavelength Selection Using Variants of Tikhonov Regularization , 2010, Applied spectroscopy.

[24]  Zhuowen Tu,et al.  Robust Point Matching via Vector Field Consensus , 2014, IEEE Transactions on Image Processing.

[25]  Sanya Liu,et al.  Blind spectral deconvolution algorithm for Raman spectrum with Poisson noise , 2014 .

[26]  S Kawata,et al.  Estimation of spectral slit width and blind deconvolution of spectroscopic data by homomorphic filtering. , 1984, Applied optics.

[27]  Ji Zhao,et al.  Non-rigid visible and infrared face registration via regularized Gaussian fields criterion , 2015, Pattern Recognit..

[28]  P. Jansson.  Deconvolution of images and spectra (2nd ed.) , 1996 .

[29]  Wolfgang Marquardt,et al.  Automatic Generation of Peak-Shaped Models , 2004, Applied spectroscopy.

[30]  Tianxu Zhang,et al.  Multi-order blind deconvolution algorithm with adaptive Tikhonov regularization for infrared spectroscopic data , 2015 .