# Beer-Lambert Autoencoder for Unsupervised Stain Representation Learning and Deconvolution in Multi-immunohistochemical Brightfield Histology Images

arXiv: https://arxiv.org/abs/2601.11336 · HTML: https://mlsanity.com/paper/2601.11336/

## Key facts

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- First posted on arXiv 16 Jan 2026.

## Abstract (arXiv)

Separating the contributions of individual chromogenic stains in RGB histology whole slide images (WSIs) is essential for stain normalization, quantitative assessment of marker expression, and cell-level readouts in immunohistochemistry (IHC). Classical Beer-Lambert (BL) color deconvolution is well-established for two- or three-stain settings, but becomes under-determined and unstable for multiplex IHC (mIHC) with K>3 chromogens. We present a simple, data-driven encoder-decoder architecture that learns cohort-specific stain characteristics for mIHC RGB WSIs and yields crisp, well-separated per-stain concentration maps. The encoder is a compact U-Net that predicts K nonnegative concentration channels; the decoder is a differentiable BL forward model with a learnable stain matrix initialized from typical chromogen hues. Training is unsupervised with a perceptual reconstruction objective augmented by loss terms that discourage unnecessary stain mixing. On a colorectal mIHC panel comprising 5 stains (H, CDX2, MUC2, MUC5, CD8) we show excellent RGB reconstruction, and significantly reduced inter-channel bleed-through compared with matrix-based deconvolution. Code and model are available at https://github.com/measty/StainQuant.git.