The rapid growth of connected vehicles creates new opportunities to exploit internet of vehicles (IoV) data for traffic state estimation (TSE), which is a key enabler of intelligent transportation systems (ITS). In this paper, we propose a cost-effective TSE framework that leverages sparse IoV data, which significantly reducing the data collection overhead associated with large-scale IoV datasets. We further analyze the impact of data sparsification and show that the induced estimation errors can be well approximated by Gaussian noise, thereby reformulating sparse IoV-based TSE as a denoising problem. To enhance estimation accuracy, we develop a spatial-temporal attention model, termed the convolutional retentive network (CRNet), which integrates convolutional neural networks (CNNs) for spatial correlation learning with a retentive network (RetNet) for temporal dependency modeling. Extensive experiments conducted on a large-scale real-world IoV dataset validate the feasibility of TSE under sparse IoV sensing conditions. Notably, even when only 5% of the data is available, CRNet achieves a mean absolute error (MAE) below 5 km/h, demonstrating both the high accuracy of the proposed approach and its practical applicability in real-world scenarios.