Accurate estimation of neuronal receptive fields is essential for understanding sensory processing in the early visual system. Yet a full characterization of receptive fields is still incomplete, especially with regard to natural visual stimuli and in complete populations of cortical neurons. While previous work has incorporated known structural properties of the early visual system, such as lateral connectivity, or imposing simple-cell-like receptive field structure, no study has exploited the fact that nearby V1 neurons share common feed-forward input from thalamus and other upstream cortical neurons. We introduce a new method for estimating receptive fields simultaneously for a population of V1 neurons, using a model-based analysis incorporating knowledge of the feed-forward visual hierarchy. We assume that a population of V1 neurons shares a common pool of thalamic inputs, and consists of two layers of simple and complex-like V1 neurons. When fit to recordings of a local population of mouse layer 2/3 V1 neurons, our model offers an accurate description of their response to natural images and significant improvement of prediction power over the current state-of-the-art methods. We show that the responses of a large local population of V1 neurons with locally diverse receptive fields can be described with surprisingly limited number of thalamic inputs, consistent with recent experimental findings. Our structural model not only offers an improved functional characterization of V1 neurons, but also provides a framework for studying the relationship between connectivity and function in visual cortical areas.