Estimating the Traffic Matrix (TM) is a critical yet resource-intensive process in network management. With the advent of deep learning models, we now have the potential to learn the inverse mapping from link loads to origin-destination (OD) flows more efficiently and accurately. However, a significant hurdle is that all current learning-based techniques necessitate a training dataset covering a comprehensive TM for a specific duration. This requirement is often unfeasible in practical scenarios. This paper addresses this complex learning challenge, specifically when dealing with incomplete and biased TM data. Our initial approach involves parameterizing the unidentified flows, thereby transforming this problem of target-deficient learning into an empirical optimization problem that integrates tomography constraints. Following this, we introduce AutoTomo, a learning-based architecture designed to optimize both the inverse mapping and the unexplored flows during the model’s training phase. We also propose an innovative observation selection algorithm, which aids network operators in gathering the most insightful measurements with limited device resources. We evaluate AutoTomo with three public traffic datasets Abilene, GÉANT and Cernet. The results reveal that AutoTomo outperforms five state-of-the-art learning-based TM estimation techniques. With complete training data, AutoTomo enhances the accuracy of the most efficient method by 15%, while it shows an improvement between 30% to 56% with incomplete training data. Furthermore, AutoTomo exhibits rapid testing speed, making it a viable tool for real-time TM estimation.