Robust spectral unmixing of multispectral Lidar waveforms

Robust Spectral Unmixing of Sparse Multispectral Lidar Waveforms Using Gamma Markov Random Fields

“…Moreover, the RMSEs gathered in Table I confirm the performance degradation as the number of detected photons decreases and that the TV-based prior model for the depth parameters mitigates this degradation (the RMSE remains below 1mm, even for the highest data sparsity). These results also illustrate the benefits of the proposed Bayesian approach for depth estimation since the RMSE obtained with the highest June 14, 2017 DRAFT data sparsity (1 photons per pixel and per band) and R-PSU-TV (RMSE = 0.92mm) is much lower than the RMSE obtained by the joint ML depth estimates proposed in [8], which processes the pixels independently (RMSE = 3.66mm). Fig.…”

“…8, depicts the results obtained by the unmixing method proposed in [8], relying on the lineariarity of the mixtures. In contrast to the proposed method, the method in [8] unmixes the pixels independently using weakly informative abundance and depth prior models. Consequently, this method is denoted by ML in Fig.…”

“…For instance, settingā i,j,r =ā r in (8) reduces to choosing the same prior, characterized by (c r ,ā r ), for all abundances associated with the rth endmember. Conversely, here we specify (8) to reflect the prior belief that abundances exhibit spatial correlations. In particular, due to the spatial organization of images, we expect the values of a i,j,r to vary smoothly from one pixel to another.…”

“…In contrast to [5], [7], the June 14, 2017 DRAFT unmixing method proposed in [6], which consists of a Metropolis-within-Gibbs sampler, assumes that there is either a single peak (whose position is estimated) or multiple peaks whose positions are known. This method has been extended in [8] to account for and identify possible deviations from the classical linear mixing model (LMM) used to estimate the amount/abundances of each endmember (assumed known) present in the scene. In this work, we further improve the robust unmixing method of [8] in order to enhance abundance and range profile estimation when there are extremely low photon counts per pixel, which is relevant to situations where the acquisition time is very restricted, e.g., in extreme low light imaging.…”

“…This method has been extended in [8] to account for and identify possible deviations from the classical linear mixing model (LMM) used to estimate the amount/abundances of each endmember (assumed known) present in the scene. In this work, we further improve the robust unmixing method of [8] in order to enhance abundance and range profile estimation when there are extremely low photon counts per pixel, which is relevant to situations where the acquisition time is very restricted, e.g., in extreme low light imaging. Specifically, we propose a new abundance prior model which promotes smooth abundance maps and we propose a depth prior model that promotes piece-wise homogeneous depth profiles.…”