Computational modeling of spectral data fitting with nonlinear distortions

Substances such as chemical compounds and biological agents are invisible to human eyes, they are usually captured by sensing equipments with their spectral fingerprints. Although spectra of pure substances can be identified by visual inspection, the spectra of their mixtures take a variety of complicated forms. Given the knowledge of spectral references of the constituent substances, the task of data fitting is to solve their weights, which usually can be solved by a least squares. Complications occur if the basis functions (reference spectra) may not be used directly to best fit the data. In fact, random spectral distortions such as shifting, compression, and expansion have been observed in some spectra. In this paper, we formulate mathematical model for such distortions and build them into data fitting algorithms. If minimal knowledge of the distortions is available, a deterministic approach termed augmented least squares is developed by fitting the spectral references together with their derivatives to the mixtures. If the distribution of the distortions is known a prior, we propose to solve the problem with maximum likelihood estimators which incorporate the distortions into the variance matrix. The proposed methods are substantiated with numerical examples including data from Raman spectroscopy, nuclear magnetic resonance, and differential optical absorption spectroscopy and show satisfactory results.

• Publication year

  2015

• Venue

  Signal, Image and Video Processing

• Publication date

  2015-01-06

• Fields of study

  Chemistry, Mathematics, Computer Science

• Identifiers
  DOI 10.1007/s11760-016-1006-2arXiv 1501.01218
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

• A perturbed linear mixing model accounting for spectral variability

  2015cited by this paper
• Hyperspectral Unmixing With Spectral Variability Using a Perturbed Linear Mixing Model

  2015influential reference
• Endmember Variability in Hyperspectral Analysis: Addressing Spectral Variability During Spectral Unmixing

  2014cited by this paper
• A non-stationary density model to separate overlapped texts in degraded documents

  2014cited by this paper
• A Convex Model for Image Registration

  2010cited by this paper
• Template Matching via l 1 Minimization and Its Application to Hyperspectral Data

  2010cited by this paper
• Differential optical absorption spectroscopy

  2008influential reference
• Robust Matched Filters for Target Detection in Hyperspectral Imaging Data

  2007cited by this paper
• Adaptive region-based image fusion using energy evaluation model for fusion decision

  2007cited by this paper
• Spectral mixture analysis for subpixel vegetation fractions in the urban environment: How to incorporate endmember variability?

  2005influential reference
• The Raman Effect: A Unified Treatment of the Theory of Raman Scattering by Molecules

  2001cited by this paper
• Mapping Chaparral in the Santa Monica Mountains Using Multiple Endmember Spectral Mixture Models

  1998cited by this paper
• Numerical analysis and estimation of the statistical error of differential optical absorption spectroscopy measurements with least-squares methods.

  1996cited by this paper
• Spectrometric Identification of Organic Compounds

  1992cited by this paper
• Iteratively Reweighted Least Squares: Algorithms, Convergence Analysis, and Numerical Comparisons

  1988cited by this paper
• An Algorithm for Least-Squares Estimation of Nonlinear Parameters

  1963cited by this paper

• Raman spectroscopic monitoring of multiproduct chemical reaction kinetics; the case of ester hydrolysis.

  2026cites this paper