Unsupervised and Supervised Algorithms for Identification of Sample Pixels in FTIR Images

TL;DR

This work tackles the challenge of distinguishing sample pixels from background in FTIR tissue images to improve spectral analysis. It introduces two unsupervised approaches—an integrated absorbance method in the $1700-1500 \mathrm{cm}^{-1}$ window and a linear-regression similarity analysis with $A(\nu) = a\bar{A}(\nu) + bP(\nu) + e(\nu)$—and a supervised deep neural network classifier for end-to-end pixel labeling. Across thyroid and kidney samples with varying thicknesses, the integrated absorbance approach performs well for THY but is less robust for thicker or contaminated kidney backgrounds, while the linear-regression method provides robust, contour-aware detection and the DNN achieves high accuracy and generalization on unseen data with rapid inference. Collectively, these methods offer robust, automated sample-pixel detection for FTIR imaging, enhancing chemical mapping and spectral histopathology in FFPE tissues and informing future FTIR signal processing workflows.

Abstract

Mid-InfraRed spectroscopy is a promising label-free technique that can offer insights into morphological and pathological alterations in biological tissues at the molecular level. Owing to the development of the Fourier Transform InfraRed (FTIR) spectrometer, combined with scanning devices, FTIR images can be produced by simultaneously acquiring spectral data from multiple spatial points, generating comprehensive chemical maps. In the data pre-processing, the identification of the sample pixels, with the background pixels excluded, is important for further effective feature extraction in FTIR images. Here, we present three algorithms realized in unsupervised and supervised approaches for the identification of the sample pixels. The algorithms demonstrate accurate prediction results of the sample and background pixels, and the supervised method further enables the automatic detection. These findings highlight thorough and robust solutions to the sample pixels detection problem in FTIR images, contributing to the FTIR signal processing and future research with FTIR images.

Figures (6)

• Figure 1: Workflow of the multivariate sample detection algorithms for FTIR images. The algorithms are realized with two approaches in this work: supervised and unsupervised frameworks. In the unsupervised approach based on integrated absorbance, the integrated absorbance of pixels is calculated between 1700-1500 cm$^{-1}$ and the sample pixels are predicted with a selected threshold. In the unsupervised approach based on linear regression, the algorithm first computes similarity scores and similarity residues of all spectra compared to the sample’s average spectrum. Dynamic thresholds of the similarity score and similarity residue for the detection of the sample pixels are then determined based on the specific characteristics and criteria of each sample. In the supervised approach, the spectrum of each pixel is fed into a well-trained neural network to predict its probability of belonging to the sample pixels. Pixels with predicted probabilities below 0.5 are automatically classified as background pixels, with others classified as sample pixels.
• Figure 2: Details of the deep neural network (DNN) for automatic sample pixels detection in FTIR images. (a) The training procedure of the DNN. The spectrum and label of each pixel are paired as an 'input-ground truth' issue. The DNN calculates the probability of the pixel belonging to the sample pixels based on the input spectrum, which is finally compared with the ground truth label for the error and its backward. (b) The backbone structure of the DNN consists of four 1D convolution layers and one full connection layer for calculating the probability from the input spectrum. The data tensors are represented with the green rectangles with the shape of Channels$\times$Lengths.
• Figure 3: Results of background detection with unsupervised linear regression approach on human thyroid tissue section samples. The integrated absorbance-based results of each sample are shown with a map of integrated absorbance (1700-1500 $cm^{-1}$), and a best prediction map. The linear regression-based results are shown with a map of similarity score, a map of similarity residue, and a best prediction map. A ground truth detection map of each sample is also shown. In the ground truth map and the best prediction map, the white-colored pixels are sample pixels, and the black ones are background. The samples from the thyroid are labeled with 'Sample 1-4' and shown in (a-d), respectively.
• Figure 4: Results of background detection with unsupervised linear regression approach on mouse kidney tissue section samples. The integrated absorbance-based results of each sample are shown with a map of integrated absorbance (1700-1500 $cm^{-1}$), and a best prediction map. The linear regression-based results are shown with a map of similarity score, a map of similarity residue, and a best prediction map. A ground truth detection map of each sample is also shown. In the ground truth map and the best prediction map, the white-colored pixels are sample pixels, and the black ones are background. The samples from the thyroid are labeled with 'Sample 5-7' and shown in (a-c), respectively.
• Figure 5: Variation of the Jaccard index between the unsupervised approach predictions and the ground truth as a function of the similarity score and similarity residue thresholds. The similarity score threshold is varied from 0 to 2, and the similarity residue threshold from 0 to 4. The resulting Jaccard index values across samples 1–7 are shown in the heatmaps (a–g). Additionally, the red stars on the plots indicate the threshold values corresponding to the maximum Jaccard index, which represent the optimal thresholds used for the results shown in Figure \ref{['fig:UnsupervisedThyroid']} and Figure \ref{['fig:UnsupervisedKidney']}.