Refocusing a plenoptic image by digital means and after the exposure has been thoroughly studied in the last years, but few efforts have been made in the direction of real time implementation in a constrained environment such as that provided by current mobile phones and tablets. In this work we address the aforementioned challenge demonstrating that a complete focal stack, comprising 31 refocused planes from a (256ff16)2 plenoptic image, can be achieved within seconds by a current SoC mobile phone platform. The election of an appropriate algorithm is the key to success. In a previous work we developed an algorithm, the fast approximate 4D:3D discrete Radon transform, that performs this task with linear time complexity where others obtain quadratic or linearithmic time complexity. Moreover, that algorithm does not requires complex number transforms, trigonometric calculus nor even multiplications nor oat numbers. Our algorithm has been ported to a multi core ARM chip on an off-the-shelf tablet running Android. A careful implementation exploiting parallelism at several levels has been necessary. The final implementation takes advantage of multi-threading in native code and NEON SIMD instructions. As a result our current implementation completes the refocusing task within seconds for a 16 megapixels image, much faster than previous attempts running on powerful PC platforms or dedicated hardware. The times consumed by the different stages of the digital refocusing are given and the strategies to achieve this result are discussed. Time results are given for a variety of environments within Android ecosystem, from the weaker/cheaper SoCs to the top of the line for 2013.