This paper presents the design and implementation of a compression system for grayscale images based on the Bandelet transform. The basis functions of the Bandelet transform are constructed as a set of vectors that indicate the directions in which the image has regular variations of gray. The compression system was designed as a SoPC and was composed of a NIOSII processor with a Cyclone IIEP2C70, a touch-panel, and a SD-Card, using 13% of the logic elements and 27% of the memory bits of the FPGA. The Wavelet filters were accelerated in hardware with NIOS II C2H Compiler, obtaining an execution time reduction of 8.8%. Experimental results show that Bandelet compression has an improvement of up to 2 dB over a Wavelet compression when the image has geometric components with high contrast.