This paper proposes a novel joint reconstruction algorithm to decode sets of correlated images from distributively compressed images. We consider a scenario where the images captured at different viewpoints are encoded independently using transform-based coding solutions (e.g., SPIHT) with a balanced rate distribution among different cameras. A central decoder jointly processes the compressed images and reconstructs an image pair by exploiting the correlation between images. The central decoder first estimates the underlying correlation model from the independently compressed images and it is eventually used for the joint signal recovery. The joint reconstruction is cast as a constrained convex optimization problem that reconstructs a total-variation (TV) smooth image pair that satisfies with the estimated correlation model. At the same time, we add constraints that force the reconstructed images to be as close as possible to the compressed views. We show by experiments that the proposed joint reconstruction scheme outperforms independent reconstruction in terms of image quality, for a given target bit rate