Online deconvolution for industrial hyperspectral imaging systems
Résumé
Hyperspectral imaging has received considerable attention in the last decade as it combines the power of digital imaging and spectroscopy. Every pixel in a hyperspectral image provides local spectral information about a scene of interest across a large number of contiguous bands. Several sensing techniques have been devised for hyperspectral imaging and can be categorized into four main groups: whiskbroom (point scan), pushbroom (line scan), tunable filter (wavelength scan), and snapshot. This paper is a first step towards the development of advanced online hyperspectral image processing methods required in industrial processes that aim at controlling and sorting input materials right after each line scanning. The aim of this paper is to address the fast online (sequential) deconvolution of hyperspectral images captured by pushbroom imaging systems. The proposed sequential deconvolution algorithm can be easily extended to whiskbroom systems.
Pushbroom imaging systems make use of 2D sensors allowing to observe the scene line-by-line at each time instant. The stream of spatial-spectral arrays is stacked to form the hyperspectral image which is a 3D data cube. A hyperspectral image may suffer from spatial distortions resulting in a loss of spatial resolution. Assuming a constant acquisition velocity, any resolution improvement results in an increase of both blurring and noise level. Thus, the corresponding distortion can be modeled by linear invariant convolution.
We introduce a least-mean-square (LMS) based framework accounting for the convolution kernel non-causality and including non-quadratic (zero attracting and piece-wise constant) regularization terms. This results in the so-called sliding block regularized LMS (SBR-LMS) which maintains a linear complexity compatible with real-time processing in industrial applications. The choice of these regularization terms is thus mainly motivated by the targeted application, namely, the inspection of objects put on a conveyor belt. At a given wavelength, the response of the conveyor after background removal is close to zero while that of the objects is supposed to be piecewise constant. A model for the algorithm mean and mean-square transient behavior is derived and the stability condition is studied.
Experiments were conducted to validate the transient behavior model with different regularization parameter values. This model allows to assess the influence of each regularization parameter. It appears that the zero-attracting property results in a faster convergence to zero than that of the algorithm without any regularization. The first order derivative regularizer is favoring the reconstruction of piecewise constant objects along the spatial dimension by decreasing the difference between two adjacent rows. However, both zero-attracting and the first order derivative properties introduce a bias on the amplitudes. More experiments showed that there exist optimal values for the different regularization parameters. Experimental results on both simulated and real hyperspectral images proved that the proposed SBR-LMS outperforms standard approaches at low SNR scenarios which is the case corresponding to ultra-fast scanning with industrial imaging systems.
Future works will focus on the automatic learning of hyperparameters. A joint online deconvolution and unmixing algorithm is also worth being studied. This is expected to yield a very low computational burden and accurate image restoration approach.