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Compressed images are frequently used to accomplish computer vision tasks. There is an extensive use of traditional image compression standards including JPEG 2000. However, they would not consider the present solution. We determined a new image compression model that was inspired by the existing research on the medical image compression model. Here, the images are filtered at the preprocessing step to eradicate the noises that exist. The images are then decomposed using discrete wavelet transform (DWT). The outcome is then vectored quantized. In this step, we employ optimisation-assisted fuzzy $c$-means clustering for vector quantisation (VQ) with codebook generation. Considering this as an optimisation issue, a new hybrid optimisation algorithm called Bald Eagle Updated Pelican Optimization with Geometric Mean weightage (BUPOGM) is introduced to solve it. The algorithm is a combination of pelican optimisation and bald eagle optimisation, respectively. Quantised coefficients are finally encoded via the Huffman encoding process, and the compressed image is represented by the resultant bits. The outcome of the proposed work is satisfactory as it performs better than the other state-of-the-art methods.