High resolution images can be acquired using a non-regular sampling sensor which consists of an underlying low resolution sensor that is covered with a non-regular sampling mask. The reconstructed high resolution image is then obtained during post-processing. Recently, it has been shown that the temporal correlation between neighboring frames can be exploited in order to enhance the reconstruction quality of non-regularly sampled video data. In this paper, a new recursive multi-frame reconstruction approach is proposed in order to further increase the reconstruction quality. By using a new reference order, previously reconstructed frames can be used for the subsequent motion estimation and a new weighting function allows for the incorporation of multiple pixels projected onto the same position. With the new recursive multi-frame approach, a visually noticeable average gain in PSNR of up to 1.13 dB with respect to a state-of-the-art single-frame reconstruction approach can be achieved. Compared to the existing multi-frame approach, a gain of 0.31 dB is possible. SSIM results show the same behavior as PSNR results. Additionally, the pre-reconstruction step of the existing multi-frame approach can be avoided and the new algorithm is, in general, capable of real-time processing.