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

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.

An analytic theory of convolutional neural network inverse problems solvers

Supervised convolutional neural networks (CNNs) are widely used to solve imaging inverse problems, achieving state-of-the-art performance in numerous applications. However, despite their empirical success, these methods are poorly understood from a theoretical perspective and often treated as black boxes. To bridge this gap, we analyze trained neural networks through the lens of the Minimum Mean Square Error (MMSE) estimator, incorporating functional constraints that capture two fundamental inductive biases of CNNs: translation equivariance and locality via finite receptive fields. Under the empirical training distribution, we derive an analytic, interpretable, and tractable formula for this constrained variant, termed Local-Equivariant MMSE (LE-MMSE). Through extensive numerical experiments across various inverse problems (denoising, inpainting, deconvolution), datasets (FFHQ, CIFAR-10, FashionMNIST), and architectures (U-Net, ResNet, PatchMLP), we demonstrate that our theory matches the neural networks outputs (PSNR $\gtrsim25$dB). Furthermore, we provide insights into the differences between \emph{physics-aware} and \emph{physics-agnostic} estimators, the impact of high-density regions in the training (patch) distribution, and the influence of other factors (dataset size, patch size, etc).

Blind Deconvolution in Astronomy: How Does a Standalone U-Net Perform?

Aims: This study investigates whether a U-Net architecture can perform standalone end-to-end blind deconvolution of astronomical images without any prior knowledge of the Point Spread Function (PSF) or noise characteristics. Our goal is to evaluate its performance against the number of training images, classical Tikhonov deconvolution and to assess its generalization capability under varying seeing conditions and noise levels. Methods: Realistic astronomical observations are simulated using the GalSim toolkit, incorporating random transformations, PSF convolution (accounting for both optical and atmospheric effects), and Gaussian white noise. A U-Net model is trained using a Mean Square Error (MSE) loss function on datasets of varying sizes, up to 40,000 images of size 48x48 from the COSMOS Real Galaxy Dataset. Performance is evaluated using PSNR, SSIM, and cosine similarity metrics, with the latter employed in a two-model framework to assess solution stability. Results: The U-Net model demonstrates effectiveness in blind deconvolution, with performance improving consistently as the training dataset size increases, saturating beyond 5,000 images. Cosine similarity analysis reveals convergence between independently trained models, indicating stable solutions. Remarkably, the U-Net outperforms the oracle-like Tikhonov method in challenging conditions (low PSNR/medium SSIM). The model also generalizes well to unseen seeing and noise conditions, although optimal performance is achieved when training parameters include validation conditions. Experiments on synthetic $C^α$ images further support the hypothesis that the U-Net learns a geometry-adaptive harmonic basis, akin to sparse representations observed in denoising tasks. These results align with recent mathematical insights into its adaptive learning capabilities.

Image Synthesis Using Spintronic Deep Convolutional Generative Adversarial Network

The computational requirements of generative adversarial networks (GANs) exceed the limit of conventional Von Neumann architectures, necessitating energy efficient alternatives such as neuromorphic spintronics. This work presents a hybrid CMOS-spintronic deep convolutional generative adversarial network (DCGAN) architecture for synthetic image generation. The proposed generative vision model approach follows the standard framework, leveraging generator and discriminators adversarial training with our designed spintronics hardware for deconvolution, convolution, and activation layers of the DCGAN architecture. To enable hardware aware spintronic implementation, the generator's deconvolution layers are restructured as zero padded convolution, allowing seamless integration with a 6-bit skyrmion based synapse in a crossbar, without compromising training performance. Nonlinear activation functions are implemented using a hybrid CMOS domain wall based Rectified linear unit (ReLU) and Leaky ReLU units. Our proposed tunable Leaky ReLU employs domain wall position coded, continuous resistance states and a piecewise uniaxial parabolic anisotropy profile with a parallel MTJ readout, exhibiting energy consumption of 0.192 pJ. Our spintronic DCGAN model demonstrates adaptability across both grayscale and colored datasets, achieving Fr'echet Inception Distances (FID) of 27.5 for the Fashion MNIST and 45.4 for Anime Face datasets, with testing energy (training energy) of 4.9 nJ (14.97~nJ/image) and 24.72 nJ (74.7 nJ/image).

CHEM: Estimating and Understanding Hallucinations in Deep Learning for Image Processing

U-Net and other U-shaped architectures have achieved significant success in image deconvolution tasks. However, challenges have emerged, as these methods might generate unrealistic artifacts or hallucinations, which can interfere with analysis in safety-critical scenarios. This paper introduces a novel approach for quantifying and comprehending hallucination artifacts to ensure trustworthy computer vision models. Our method, termed the Conformal Hallucination Estimation Metric (CHEM), is applicable to any image reconstruction model, enabling efficient identification and quantification of hallucination artifacts. It offers two key advantages: it leverages wavelet and shearlet representations to efficiently extract hallucinations of image features and uses conformalized quantile regression to assess hallucination levels in a distribution-free manner. Furthermore, from an approximation theoretical perspective, we explore the reasons why U-shaped networks are prone to hallucinations. We test the proposed approach on the CANDELS astronomical image dataset with models such as U-Net, SwinUNet, and Learnlets, and provide new perspectives on hallucination from different aspects in deep learning-based image processing.

Hierarchical Spatial-Frequency Aggregation for Spectral Deconvolution Imaging

Computational spectral imaging (CSI) achieves real-time hyperspectral imaging through co-designed optics and algorithms, but typical CSI methods suffer from a bulky footprint and limited fidelity. Therefore, Spectral Deconvolution imaging (SDI) methods based on PSF engineering have been proposed to achieve high-fidelity compact CSI design recently. However, the composite convolution-integration operations of SDI render the normal-equation coefficient matrix scene-dependent, which hampers the efficient exploitation of imaging priors and poses challenges for accurate reconstruction. To tackle the inherent data-dependent operators in SDI, we introduce a Hierarchical Spatial-Spectral Aggregation Unfolding Framework (HSFAUF). By decomposing subproblems and projecting them into the frequency domain, HSFAUF transforms nonlinear processes into linear mappings, thereby enabling efficient solutions. Furthermore, to integrate spatial-spectral priors during iterative refinement, we propose a Spatial-Frequency Aggregation Transformer (SFAT), which explicitly aggregates information across spatial and frequency domains. By integrating SFAT into HSFAUF, we develop a Transformer-based deep unfolding method, \textbf{H}ierarchical \textbf{S}patial-\textbf{F}requency \textbf{A}ggregation \textbf{U}nfolding \textbf{T}ransformer (HSFAUT), to solve the inverse problem of SDI. Systematic simulated and real experiments show that HSFAUT surpasses SOTA methods with cheaper memory and computational costs, while exhibiting optimal performance on different SDI systems.

DeblurSDI: Blind Image Deblurring Using Self-diffusion

Blind image deconvolution is a challenging ill-posed inverse problem, where both the latent sharp image and the blur kernel are unknown. Traditional methods often rely on handcrafted priors, while modern deep learning approaches typically require extensive pre-training on large external datasets, limiting their adaptability to real-world scenarios. In this work, we propose DeblurSDI, a zero-shot, self-supervised framework based on self-diffusion (SDI) that requires no prior training. DeblurSDI formulates blind deconvolution as an iterative reverse self-diffusion process that starts from pure noise and progressively refines the solution. At each step, two randomly-initialized neural networks are optimized continuously to refine the sharp image and the blur kernel. The optimization is guided by an objective function combining data consistency with a sparsity-promoting L1-norm for the kernel. A key innovation is our noise scheduling mechanism, which stabilizes the optimization and provides remarkable robustness to variations in blur kernel size. These allow DeblurSDI to dynamically learn an instance-specific prior tailored to the input image. Extensive experiments demonstrate that DeblurSDI consistently achieves superior performance, recovering sharp images and accurate kernels even in highly degraded scenarios.

Null-Space Diffusion Distillation for Efficient Photorealistic Lensless Imaging

State-of-the-art photorealistic reconstructions for lensless cameras often rely on paired lensless-lensed supervision, which can bias models due to lens-lensless domain mismatch. To avoid this, ground-truth-free diffusion priors are attractive; however, generic formulations tuned for conventional inverse problems often break under the noisy, highly multiplexed, and ill-posed lensless deconvolution setting. We observe that methods which separate range-space enforcement from null-space diffusion-prior updates yield stable, realistic reconstructions. Building on this, we introduce Null-Space Diffusion Distillation (NSDD): a single-pass student that distills the null-space component of an iterative DDNM+ solver, conditioned on the lensless measurement and on a range-space anchor. NSDD preserves measurement consistency and achieves photorealistic results without paired supervision at a fraction of the runtime and memory. On Lensless-FFHQ and PhlatCam, NSDD is the second fastest, behind Wiener, and achieves near-teacher perceptual quality (second-best LPIPS, below DDNM+), outperforming DPS and classical convex baselines. These results suggest a practical path toward fast, ground-truth-free, photorealistic lensless imaging.

Building Trust in Virtual Immunohistochemistry: Automated Assessment of Image Quality

Deep learning models can generate virtual immunohistochemistry (IHC) stains from hematoxylin and eosin (H&E) images, offering a scalable and low-cost alternative to laboratory IHC. However, reliable evaluation of image quality remains a challenge as current texture- and distribution-based metrics quantify image fidelity rather than the accuracy of IHC staining. Here, we introduce an automated and accuracy grounded framework to determine image quality across sixteen paired or unpaired image translation models. Using color deconvolution, we generate masks of pixels stained brown (i.e., IHC-positive) as predicted by each virtual IHC model. We use the segmented masks of real and virtual IHC to compute stain accuracy metrics (Dice, IoU, Hausdorff distance) that directly quantify correct pixel - level labeling without needing expert manual annotations. Our results demonstrate that conventional image fidelity metrics, including Frechet Inception Distance (FID), peak signal-to-noise ratio (PSNR), and structural similarity (SSIM), correlate poorly with stain accuracy and pathologist assessment. Paired models such as PyramidPix2Pix and AdaptiveNCE achieve the highest stain accuracy, whereas unpaired diffusion- and GAN-based models are less reliable in providing accurate IHC positive pixel labels. Moreover, whole-slide images (WSI) reveal performance declines that are invisible in patch-based evaluations, emphasizing the need for WSI-level benchmarks. Together, this framework defines a reproducible approach for assessing the quality of virtual IHC models, a critical step to accelerate translation towards routine use by pathologists.

Deep learning EPI-TIRF cross-modality enables background subtraction and axial super-resolution for widefield fluorescence microscopy

The resolving ability of wide-field fluorescence microscopy is fundamentally limited by out-of-focus background owing to its low axial resolution, particularly for densely labeled biological samples. To address this, we developed ET2dNet, a deep learning-based EPI-TIRF cross-modality network that achieves TIRF-comparable background subtraction and axial super-resolution from a single wide-field image without requiring hardware modifications. The model employs a physics-informed hybrid architecture, synergizing supervised learning with registered EPI-TIRF image pairs and self-supervised physical modeling via convolution with the point spread function. This framework ensures exceptional generalization across microscope objectives, enabling few-shot adaptation to new imaging setups. Rigorous validation on cellular and tissue samples confirms ET2dNet's superiority in background suppression and axial resolution enhancement, while maintaining compatibility with deconvolution techniques for lateral resolution improvement. Furthermore, by extending this paradigm through knowledge distillation, we developed ET3dNet, a dedicated three-dimensional reconstruction network that produces artifact-reduced volumetric results. ET3dNet effectively removes out-of-focus background signals even when the input image stack lacks the source of background. This framework makes axial super-resolution imaging more accessible by providing an easy-to-deploy algorithm that avoids additional hardware costs and complexity, showing great potential for live cell studies and clinical histopathology.