Inverse problems are essential to imaging applications. In this letter, we propose a model-based deep learning network, named FISTA-Net, by combining the merits of interpretability and generality of the model-based Fast Iterative Shrinkage/Thresholding Algorithm (FISTA) and strong regularization and tuning-free advantages of the data-driven neural network. By unfolding the FISTA into a deep network, the architecture of FISTA-Net consists of multiple gradient descent, proximal mapping, and momentum modules in cascade. Different from FISTA, the gradient matrix in FISTA-Net can be updated during iteration and a proximal operator network is developed for nonlinear thresholding which can be learned through end-to-end training. Key parameters of FISTA-Net including the gradient step size, thresholding value and momentum scalar are tuning-free and learned from training data rather than hand-crafted. We further impose positive and monotonous constraints on these parameters to ensure they converge properly. The experimental results, evaluated both visually and quantitatively, show that the FISTA-Net can optimize parameters for different imaging tasks, i.e. Electromagnetic Tomography (EMT) and X-ray Computational Tomography (X-ray CT). It outperforms the state-of-the-art model-based and deep learning methods and exhibits good generalization ability over other competitive learning-based approaches under different noise levels.

Multifrequency electrical impedance tomography (mfEIT) is an emerging biomedical imaging modality to reveal frequency-dependent conductivity distributions in biomedical applications. Conventional model-based image reconstruction methods suffer from low spatial resolution, unconstrained frequency correlation, and high computational cost. Deep learning has been extensively applied in solving the EIT inverse problem in biomedical and industrial process imaging. However, most existing learning-based approaches deal with the single-frequency setup, which is inefficient and ineffective when extended to the multifrequency setup. This article presents a multiple measurement vector (MMV) model-based learning algorithm named MMV-Net to solve the mfEIT image reconstruction problem. MMV-Net considers the correlations between mfEIT images and unfolds the update steps of the Alternating Direction Method of Multipliers for the MMV problem (MMV-ADMM). The nonlinear shrinkage operator associated with the weighted $l_{2,1}$ regularization term of MMV-ADMM is generalized in MMV-Net with a cascade of a Spatial Self-Attention module and a Convolutional Long Short-Term Memory (ConvLSTM) module to better capture intrafrequency and interfrequency dependencies. The proposed MMV-Net was validated on our Edinburgh mfEIT Dataset and a series of comprehensive experiments. The results show superior image quality, convergence performance, noise robustness, and computational efficiency against the conventional MMV-ADMM and the state-of-the-art deep learning methods.

Spatial proteomics enables high-resolution mapping of protein expression and can transform our understanding of biology and disease. However, major challenges remain for clinical translation, including cost, complexity and scalability. Here we present H&E to protein expression (HEX), an AI model designed to computationally generate spatial proteomics profiles from standard histopathology slides. Trained and validated on 819,000 histopathology image tiles with matched protein expression from 382 tumor samples, HEX accurately predicts the expression of 40 biomarkers encompassing immune, structural and functional programs. HEX demonstrates substantial performance gains over alternative methods for protein expression prediction from H&E images. We develop a multimodal data integration approach that combines the original H&E image and AI-derived virtual spatial proteomics to enhance outcome prediction. Applied to six independent non-small-cell lung cancer cohorts totaling 2,298 patients, HEX-enabled multimodal integration improved prognostic accuracy by 22% and immunotherapy response prediction by 24–39% compared with conventional clinicopathological and molecular biomarkers. Biological interpretation revealed spatially organized tumor–immune niches predictive of therapeutic response, including the co-localization of T helper cells and cytotoxic T cells in responders, and immunosuppressive tumor-associated macrophage and neutrophil aggregates in non-responders. HEX provides a low-cost and scalable approach to study spatial biology and enables the discovery and clinical translation of interpretable biomarkers for precision medicine.

Accurate prognosis prediction is essential for guiding cancer treatment and improving patient outcomes. While recent studies have demonstrated the potential of histopathological images in survival analysis, existing models are typically developed in a cancer-specific manner, lack extensive external validation, and often rely on molecular data that are not routinely available in clinical practice. To address these limitations, we present PROGPATH, a unified model capable of integrating histopathological image features with routinely collected clinical variables to achieve pancancer prognosis prediction. PROGPATH employs a weakly supervised deep learning architecture built upon the foundation model for image encoding. Morphological features are aggregated through an attention-guided multiple instance learning module and fused with clinical information via a cross-attention transformer. A router-based classification strategy further refines the prediction performance. PROGPATH was trained on 7999 whole-slide images (WSIs) from 6,670 patients across 15 cancer types, and extensively validated on 17 external cohorts with a total of 7374 WSIs from 4441 patients, covering 12 cancer types from 8 consortia and institutions across three continents. PROGPATH achieved consistently superior performance compared with state-of-the-art multimodal prognosis prediction models. It demonstrated strong generalizability across cancer types and robustness in stratified subgroups, including early- and advanced-stage patients, treatment cohorts (radiotherapy and pharmaceutical therapy), and biomarker-defined subsets. We further provide model interpretability by identifying pathological patterns critical to PROGPATH’s risk predictions, such as the degree of cell differentiation and extent of necrosis. Together, these results highlight the potential of PROGPATH to support pancancer outcome prediction and inform personalized cancer management strategies.