Four-dimensional (4D) computed tomography (CT) image acquisition is a useful technique in radiation treatment planning and interventional radiology in that it can account for respiratory motion of lungs. Current 4D lung reconstruction techniques have limitations in either spatial or temporal resolution. In addition, most of these techniques rely on auxiliary surrogates to relate the time of CT scan to the patient's respiratory phase. In this paper, we propose a novel 4D CT lung reconstruction and deformation estimation algorithm. Our algorithm is purely image based. The algorithm can reconstruct high quality 4D images even if the original images are acquired under irregular respiratory motion. The algorithm is validated using synthetic 4D lung data. Experimental results from a swine study data are also presented.