This article presents the theory behind a model for a two-stage analog network for edge detection and image reconstruction to be implemented in analog VLSI. Edges are detected in the first stage using the multiscale veto rule, which states that an edge exists only if it can pass a threshold test for each of a set of smoothing filters of decreasing bandwidth. The image is reconstructed in the second stage from the brightness values at the pixels between which edges occur. The effect of the multiscale veto rule is that noise is removed with the efficiency of the narrowest-band smoothing filter, while edges are well-localized to feature boundaries without having to identify maxima in the magnitude of the gradient. Unlike previous analog models for edge detection and reconstruction, there are no problems of local minima, and for any given set of parameters, there is a unique solution. The reconstructed images appear natural and are very similar visually to the originals.