This study presents the design and implementation of efficient architectures for finite Radon transform (FRAT) on a field programmable gate array (FPGA). FPGA-based architectures with two design strategies have been proposed: direct implementation of pseudo-code with a sequential or pipelined description, and a block random access memory-based approach. Various medical images modalities have been deployed for both software evaluation and hardware implementation. Xilinx DSP tool has been used to improve the implementation time and reduce the design cycle and the Xilinx software has been used for generating a hardware description language from a high-level MATLAB description. Objective evaluation of image denoising using FRAT is carried out and demonstrates promising results. Moreover, the impact of different block sizes on image reconstruction has been analysed. Performance analysis in terms of area, maximum frequency and throughput is presented and reveals significant achievements.