Recently, compressed-sensing based algorithms have enabled volume reconstruction from projection images acquired over a relatively small angle (θ < 20°). These methods enable accurate depth estimation of surgical tools with respect to anatomical structures. However, they are computationally expensive and time consuming, rendering them unattractive for image-guided interventions. We propose an alternative approach for depth estimation of biopsy needles during image-guided interventions, in which we split the problem into two parts and solve them independently: needle-depth estimation and volume reconstruction. The complete proposed system consists of the previous two steps, preceded by needle extraction. First, we detect the biopsy needle in the projection images and remove it by interpolation. Next, we exploit epipolar geometry to find point-to-point correspondences in the projection images to triangulate the 3D position of the needle in the volume. Finally, we use the interpolated projection images to reconstruct the local anatomical structures and indicate the position of the needle within this volume. For validation of the algorithm, we have recorded a full CT scan of a phantom with an inserted biopsy needle. The performance of our approach ranges from a median error of 2.94 mm for an distributed viewing angle of 1° down to an error of 0.30 mm for an angle larger than 10°. Based on the results of this initial phantom study, we conclude that multi-view geometry offers an attractive alternative to time-consuming iterative methods for the depth estimation of surgical tools during C-arm-based image-guided interventions.