Online spectral unmixing in gamma-ray spectrometry.

We introduced in a previous paper a time-dependent full-spectrum analysis algorithm speeding up the estimation of the activity of the radionuclides present in a sample. In this paper, we present a new version of the algorithm allowing online estimation. It uses only on a buffer of few segments while keeping the time information by using a time dependent regularization, thus reducing the size of the data matrices and the length of the processing of each iteration. The algorithm is optimized and tested on both simulated and measured spectra of aerosol samples.

Analysis of gamma-ray spectra with spectral unmixing - Part I: Determination of the characteristic limits (decision threshold and statistical uncertainty) for measurements of environmental aerosol filters.

Poisson-statistics based spectral unmixing has been shown to be an efficient analysis tool for the radionuclides activity estimation from gamma-ray spectrometry measurements. However, the calculation of the corresponding characteristic limits has not been investigated so far. In this paper, we present the quantification of the decision threshold and the limits of the coverage interval for the metrological use of such spectral unmixing algorithms. The proposed approach is evaluated and validated with simulated spectra of HPGe and NaI measurements by comparing the results to characteristic limits calculated from Monte-Carlo simulations. We focus particularly on the validation of the method for the metrological analysis of environmental measurements, for which the low-level activity quantification requires an accurate characteristic limits determination. Along with the instrument calibration, we establish a metrological analysis tool by using the spectral unmixing algorithm for environmental aerosol filters measured by gamma-ray spectrometry.

Analysis of gamma-ray spectra with spectral unmixing, Part II: Recalibration for the quantitative analysis of HPGe measurements.

In the context of radioactivity measurements, the quantitative analysis of a gamma-ray spectrum depends on the analysis algorithm. To that end, we recently introduced a Poisson statistics-based spectral unmixing approach. However, it also relies on a proper instrument recalibration as well as on an uncertainty estimation, for which no solution has been proposed so far. The goal of this article is twofold: i) we first present a novel method to correct for the instrument calibration of an HPGe detection system, which is tailored to spectral unmixing algorithms, and ii) we apply this new approach to the quantitative analysis of real data as well as on the evaluation of the uncertainty. Along with the characteristic limits determination investigated, this paper introduces the first full metrological analysis sequence of aerosol filter measurements based on spectral unmixing, which allows to quantify both the radionuclides' activities and their associated uncertainties.

Polarizer-free two-pixel polarimetric camera by compressive sensing.

We propose an original concept of compressive sensing (CS) polarimetric imaging based on a digital micromirror (DMD) array and two single-pixel detectors, without using any polarizer. The polarimetric sensitivity of the proposed setup is due to the tiny difference in Fresnel's coefficients of reflecting mirrors, which is exploited here to form an original reconstruction problem including a CS problem and a source-separation task. We show that a two-step approach, tackling each problem successively, is outperformed by a dedicated combined reconstruction method, which is demonstrated in this paper and preferably implemented through a reweighted fast iterative shrinkage-thresholding algorithm. The combined reconstruction approach is then further improved by including physical constraints specific to the polarimetric imaging context considered, which are implemented in an original constrained generalized forward-backward algorithm. Numerical simulations demonstrate the efficiency of the two-pixel CS polarimetric imaging setup at retrieving polarimetric contrast data with significant compression rate and good reconstruction quality. The influence of experimental imperfections of the DMD is also analyzed through numerical simulations, and 2D polarimetric imaging reconstruction results are finally presented.

Compressive fluorescence microscopy for biological and hyperspectral imaging.

The mathematical theory of compressed sensing (CS) asserts that one can acquire signals from measurements whose rate is much lower than the total bandwidth. Whereas the CS theory is now well developed, challenges concerning hardware implementations of CS-based acquisition devices--especially in optics--have only started being addressed. This paper presents an implementation of compressive sensing in fluorescence microscopy and its applications to biomedical imaging. Our CS microscope combines a dynamic structured wide-field illumination and a fast and sensitive single-point fluorescence detection to enable reconstructions of images of fluorescent beads, cells, and tissues with undersampling ratios (between the number of pixels and number of measurements) up to 32. We further demonstrate a hyperspectral mode and record images with 128 spectral channels and undersampling ratios up to 64, illustrating the potential benefits of CS acquisition for higher-dimensional signals, which typically exhibits extreme redundancy. Altogether, our results emphasize the interest of CS schemes for acquisition at a significantly reduced rate and point to some remaining challenges for CS fluorescence microscopy.

Hyperspectral BSS using GMCA with spatio-spectral sparsity constraints.

Generalized morphological component analysis (GMCA) is a recent algorithm for multichannel data analysis which was used successfully in a variety of applications including multichannel sparse decomposition, blind source separation (BSS), color image restoration and inpainting. Building on GMCA, the purpose of this contribution is to describe a new algorithm for BSS applications in hyperspectral data processing. It assumes the collected data is a mixture of components exhibiting sparse spectral signatures as well as sparse spatial morphologies, each in specified dictionaries of spectral and spatial waveforms. We report on numerical experiments with synthetic data and application to real observations which demonstrate the validity of the proposed method.

Sparsity and morphological diversity in blind source separation.

Over the last few years, the development of multichannel sensors motivated interest in methods for the coherent processing of multivariate data. Some specific issues have already been addressed as testified by the wide literature on the so-caIled blind source separation (BSS) problem. In this context, as clearly emphasized by previous work, it is fundamental that the sources to be retrieved present some quantitatively measurable diversity. Recently, sparsity and morphological diversity have emergedas a novel and effective source of diversity for BSS. Here, we give some new and essential insights into the use of sparsity in source separation, and we outline the essential role of morphological diversity as being a source of diversity or contrast between the sources. This paper introduces a new BSS method coined generalized morphological component analysis (GMCA) that takes advantages of both morphological diversity and sparsity, using recent sparse overcomplete or redundant signal representations. GMCA is a fast and efficient BSS method. We present arguments and a discussion supporting the convergence of the GMCA algorithm. Numerical results in multivariate image and signal processing are given illustrating the good performance of GMCA and its robustness to noise.

Morphological component analysis: an adaptive thresholding strategy.

In a recent paper, a method called morphological component analysis (MCA) has been proposed to separate the texture from the natural part in images. MCA relies on an iterative thresholding algorithm, using a threshold which decreases linearly towards zero along the iterations. This paper shows how the MCA convergence can be drastically improved using the mutual incoherence of the dictionaries associated to the different components. This modified MCA algorithm is then compared to basis pursuit, and experiments show that MCA and BP solutions are similar in terms of sparsity, as measured by the l1 norm, but MCA is much faster and gives us the possibility of handling large scale data sets.