Anemia diagnosis is crucial for pediatric patients due to its impact on growth and development. Traditional methods, like blood tests, are effective but pose challenges, such as discomfort, infection risk, and frequent monitoring difficulties, underscoring the need for non-intrusive diagnostic methods. In light of this, this study proposes a novel method that combines image processing with learning-driven data representation and model behavior for non-intrusive anemia diagnosis in pediatric patients. The contributions of this study are threefold. First, it uses an image-processing pipeline to extract 181 features from 13 categories, with a feature-selection process identifying the most crucial data for learning. Second, a deep multilayered network based on long short-term memory (LSTM) is utilized to train a model for classifying images into anemic and non-anemic cases, where hyperparameters are optimized using Bayesian approaches. Third, the trained LSTM model is integrated as a layer into a learning model developed based on recurrent expansion rules, forming a part of a new deep network called a recurrent expansion network (RexNet). RexNet is designed to learn data representations akin to traditional deep-learning methods while also understanding the interaction between dependent and independent variables. The proposed approach is applied to three public datasets, namely conjunctival eye images, palmar images, and fingernail images of children aged up to 6 years. RexNet achieves an overall evaluation of 99.83 ± 0.02% across all classification metrics, demonstrating significant improvements in diagnostic results and generalization compared to LSTM networks and existing methods. This highlights RexNet's potential as a promising alternative to traditional blood-based methods for non-intrusive anemia diagnosis.