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Estimating temporal patterns in travel times along road segments in urban settings is of central importance to traffic engineers and city planners. In this work, we propose a methodology to leverage coarse-grained and aggregated travel time data to estimate the street-level travel times of a given metropolitan area. Our main focus is to estimate travel times along the arterial road segments where relevant data are often unavailable. The central idea of our approach is to leverage easy-to-obtain, aggregated data sets with broad spatial coverage, such as the data published by Uber Movement, as the fabric over which other expensive, fine-grained datasets, such as loop counter and probe data, can be overlaid. Our proposed methodology uses a graph representation of the road network and combines several techniques such as graph-based routing, trip sampling, graph sparsification, and least-squares optimization to estimate the street-level travel times. Using sampled trips and weighted shortest-path routing, we iteratively solve constrained least-squares problems to obtain the travel time estimates. We demonstrate our method on the Los Angeles metropolitan-area street network, where aggregated travel time data is available for trips between traffic analysis zones. Additionally, we present techniques to scale our approach via a novel graph pseudo-sparsification technique.