Original-domain Tikhonov regularization and non-negativity constraint improve resolution of spectrophotometric analyses

Szczeciński, Leszek; Morawski, Roman Z.; Barwicz, A.

doi:10.1016/s0263-2241(96)00031-0

Cited by 12 publications

(8 citation statements)

References 7 publications

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“…Non-negative least square (NNLS) method has been exploited and found useful for spectrum estimation in the past [8], [9], [14] and recently [15], [18]. Based on our experiment, satisfactory results were obtained by solving a system of linear equations based on NNLS method, with the regularization parameter being selected by the L-curve criterion.…”

Section: Introductionmentioning

confidence: 86%

“…The filter factor is close to zero when and is close to one when . For higher order regularization, generalized SVD method can be applied, and the solution can be obtained in the form similar to (9). Therefore, for a given value of , the Tikhonov regularization provide a systematic mean to adaptively select the weighting of each basis component for robust matrix inverse.…”

Section: Regularizationmentioning

confidence: 99%

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Filter-Based Miniature Spectrometers: Spectrum Reconstruction Using Adaptive Regularization

Kurokawa¹,

Choi²,

2011

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Miniature spectrometers provide a cost and size advantage over traditional spectrometers. However, unlike traditional spectrometers in which appropriate dispersive optics and/or interferometric devices are well-developed, miniature spectrometers usually do not have ideal (or close to ideal) wavelength-specific filtering mechanism to resolve the power of the input spectrum at specified wavelengths. Hence, the raw outputs from the filtering mechanism may not be adequate to represent spectra of measured objects. The nonideal filtering mechanism makes reconstruction process necessary. In this work, the method of Tikhonov regularization for stabilizing the solution of inverse problems is applied to a prototype filter-based nano-optic spectrum sensor from nanoLambda. L-curve criterion and generalized cross validation (GCV) criterion for adaptively selecting the regularization parameter are examined. Satisfactory results are obtained by exploiting non-negative constraints on the reconstructed spectrum, with the regularization parameter being selected by the L-curve criterion. As a result, low-cost miniature spectrometer on-a-chip can be realized.

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Section: Introductionmentioning

confidence: 86%

Section: Regularizationmentioning

confidence: 99%

Filter-Based Miniature Spectrometers: Spectrum Reconstruction Using Adaptive Regularization

Kurokawa¹,

Choi²,

2011

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“…This may be achieved by integrating, into the operator R , some a priori knowledge about the expected solution, in particular the information on its positivity . The numerical power of this stratagem has been demonstrated for many methods of spectrum reconstruction -by numerous researchers, including the authors of this paper [26][27][28][29][30] -and is still subject to further investigation, e.g. [31].…”

Section: Problem Identificationmentioning

confidence: 99%

Signal Decomposition and Pseudo-baseline Optimization in Spectrum Reconstruction

Morawski¹,

Miekina²

2006

2006 IEEE Instrumentation and Measurement Technology Conference Proceedings

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The problem of reconstruction of high-resolution spectra on the basis of low-resolution data, provided by spectrophotometers, is addressed. It is shown that the performance of the algorithms for spectrum reconstruction with an in-built positivity constraint deteriorates for the data containing a considerable baseline (background). A new method for overcoming that limitation is proposed. It consists in subtraction of a rough estimate of the baseline (called pseudo-baseline) from the data, reconstruction of spectrum on the basis of the data modified in this way, and restoration of the pseudobaseline in the final result of spectrum reconstruction. The proposed amelioration is illustrated by means of an algorithm of spectrum reconstruction, based on the Jansson method of deconvolution.

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“…3.12. In order to make the EIT problem wellposed, generally, the regularization techniques [16,17,22,27,117,195,220] are incorporated into the EIT reconstruction algorithm by including a regularizing term in the object function. The object function, therefore, is redefined with regularization parameters as [16,17,22,27,220]:…”

Section: Conductivity Reconstructionmentioning

confidence: 99%

Noninvasive Electromagnetic Methods for Brain Monitoring: A Technical Review

Bera

2014

Brain-Computer Interfaces

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Original-domain Tikhonov regularization and non-negativity constraint improve resolution of spectrophotometric analyses

Cited by 12 publications

References 7 publications

Filter-Based Miniature Spectrometers: Spectrum Reconstruction Using Adaptive Regularization

Filter-Based Miniature Spectrometers: Spectrum Reconstruction Using Adaptive Regularization

Signal Decomposition and Pseudo-baseline Optimization in Spectrum Reconstruction

Noninvasive Electromagnetic Methods for Brain Monitoring: A Technical Review

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