Efficient architectures and implementations of median filters have been well investigated in the past. In this article, we focus on median filters for very big scientific applications with very large windows and an infinite stream of data, inspired by big data needs in the Square Kilometre Array (SKA) pulsar search engine, but transferable to other big data domains. We propose a novel approach for very large rectangular windows on an FPGA accelerator device able to support the processing of infinite streams of data. OpenCL is used for rapid parameter sweeping and design space exploration based on a pipelined model of the system. Evaluation on a host/accelerator system with an Arria 10 device surpassed 64 million values processed per second considered for the SKA real time requirement, achieving 83.4M value/s while reading from/writing to disk. These results are compared with a state-of-the-art software implementation only achieving 41M value/s for over twice the total system energy cost.