Extended Blind End-Member and Abundance Extraction for Biomedical Imaging Applications

Abstract

In some applications of biomedical imaging, a linear mixture model can represent the constitutive elements (end-members) and their contributions (abundances) per pixel of the image. In this work, the extended blind end-member and abundance extraction (EBEAE) methodology is mathematically formulated to address the blind linear unmixing (BLU) problem subject to positivity constraints in optical measurements. The EBEAE algorithm is based on a constrained quadratic optimization and an alternated least-squares strategy to jointly estimate end-members and their abundances. In our proposal, a local approach is used to estimate the abundances of each end-member by maximizing their entropy, and a global technique is adopted to iteratively identify the end-members by reducing the similarity among them. All the cost functions are normalized, and four initialization approaches are suggested for the end-members matrix. Synthetic datasets are used first for the EBEAE validation at different noise types and levels, and its performance is compared to state-of-the-art algorithms in BLU. In a second stage, three experimental biomedical imaging applications are addressed with EBEAE: m-FLIM for chemometric analysis in oral cavity samples, OCT for macrophages identification in post-mortem artery samples, and hyper-spectral images for in-vivo brain tissue classification and tumor identification. In our evaluations, EBEAE was able to provide a quantitative analysis of the samples with none or minimal a priori information.INDEX TERMS Blind linear unmixing, constrained optimization, fluorescence lifetime imaging microscopy, hyperspectral imaging, optical coherence tomography.

Blind deconvolution estimation by multi-exponential models and alternated least squares approximations: Free-form and sparse approach

“…The inverse problems in Eqs (16) and (19) involve nonlinear interactions among the free parameters of the InstR , and those involved in the FluoIR or τ . To tackle these problems, we applied ALS approaches similar to [ 21 ] and [ 38 , 39 ], where we estimate a solution for the FluoIR components while fixing the InstR, and vice versa until convergence.…”

“…or τ. To tackle these problems, we applied ALS approaches similar to [21] and [38,39], where we estimate a solution for the FluoIR components while fixing the InstR, and vice versa until convergence.…”

“…There are different strategies to solve this inverse problem, usually the InstR is assumed known or measured a priori, and then carefully aligned with the FluoIRs to avoid bias in the estimations. Other strategies quantify FLIM data by analyzing the FluoDs with a linear unmixing approach [21][22][23][24][25], or in a lower-dimensional domain using the phasor approach [26][27][28].…”

Classification of Hyperspectral In Vivo Brain Tissue Based on Linear Unmixing

“…The methodology called extended blind end-member and abundance extraction (EBEAE), proposed in [26], allows estimating end-members and their abundances by a linear mixing model in non-negative datasets. In addition, the BLU process by EBEAE is controlled by hyperparameters that adjust the resulting similarity among end-members and the entropy of the abundances.…”

“…Another recent proposal is the extended blind end-member and abundance extraction (EBEAE) methodology that can be used for BLU in non-negative datasets by considering linearly independent end-members and normalized abundances. This method was previously used for biomedical imaging applications, including m-FLIM (multi-spectral fluorescence lifetime imaging) for chemometric analysis in oral cavity samples, OCT (optical coherence tomography) for macrophage identification in post-mortem artery samples, and in vivo brain tissue classification by using HSI [26].…”