In this paper, we have presented Discrete Wavelet Transform (DWT) based Fast Output Generating Set Partitioning in Hierarchical Trees (FOGSPIHT) algorithm for MRI brain image compression. The FOGSPIHT is scalable, faster, and robust algorithm. Image compression is an important technique that enables fast and high throughput imaging applications by reducing the storage space or transmission bandwidth. DWT transforms the image to get a set of coefficients that are used for efficient compression. The Set Partitioning In Hierarchical Trees (SPIHT) algorithm is an efficient algorithm used for DWT based image compression. The limitations of SPIHT coding are the complexity and memory requirements. To reduce the complexity, we propose the FOGSPIHT algorithm that works on the basic principles of SPIHT. The FOGSPIHT algorithm works on coefficients that are converted to bit planes. FOGSPIHT eliminates the comparison operations in the compression process of SPIHT by simple logical operations on bits. The values of Mean Square Error (MSE), Peak Signal to Noise Ratio (PSNR), and Structural Similarity Index Measure (SSIM) are calculated and plotted against Compression Ratio (CR). The result obtained with the FOGSPIHT algorithm is equal to or better than the SPIHT algorithm. The FOGSPIHT algorithm is faster which has reduced encoding and decoding time. The implementation of the FOGSPIHT algorithm with an 8x8 image DWT coefficient on FPGA requires the lower amount of resource and power requirements in comparison with the SPIHT algorithm.