The issue of image compression continues to be a subject of ongoing research within the domain of image processing, particularly in the context of medical applications. The quality of the decompressed image can vary depending on the accuracy of the compression technique, resulting in either fine or distorted details. Therefore, the diagnostic procedure performed by medical professionals is contingent upon the precision of the compression and decompression process. In addition, the compression of medical images serves to decrease the amount of storage required, thereby enabling faster transmission over computer networks through the reduction of their bit size. This paper proposes a hybrid mix of the discrete wavelet transform (DWT) technique and vector quantization (VQ) to improve the compression technique of medical images. The aim of the proposed compression technique is to preserve diagnostic image information while achieving a high compression ratio. First, noise in medical images is caused by salt pepper noise. At the same time, the edges of the images are maintained in sharpness and context. Then, a lossless compression method is applied to the wavelet coefficients of the subband with the lowest frequency, while the thresholding method was used to efficiently construct coefficients for high-frequency sub-bands. This process will produce a traditional VQ, which is estimated via the Genetic Algorithm (GA) with fuzzy clustering. While Arithmetic encoded theory was being utilized to quantize coefficients, the proposed compression technique was evaluated by dividing the image into two levels and three levels of sub-bands, respectively, in two different scenarios. Comparing the decompressed image to the filtered image by means of different evaluation metrics, the proposed method can enhance compression performance and strike a balance between compression ratio and image visual quality.