Compression of images with a mathematical approach based on sine and cosine equations and vector quantization (VQ)

Compressing the image causes less memory to be used to store the images. Compressing images increases the transmission speed of compressed images in the network. Vector quantization (VQ) is one of the image compression methods. The challenge of the vector quantization method for compression is the non-optimization of the codebooks. Codebook optimization increases the quality of compressed images and reduces the volume of compressed images. Various methods of swarm intelligence and meta-heuristics are used to improve the vector quantization algorithm, but using meta-heuristic methods based on mathematical sciences has less history. This paper uses an improved sine–cosine algorithm (SCA) version to optimize the vector quantization algorithm and reduce the compression error. The reason for using the SCA algorithm in image compression is the balance between the search for exploration and exploitation search by sine and cosine functions, which makes it less likely to get caught in local optima. The proposed method to reduce the calculation error of the SCA algorithm uses spiral trigonometric functions and a new mathematical helix. The proposed method searches for optimal solutions with spiral and snail searches, increasing the chances of finding more optimal solutions. The proposed method aims to find a more optimal codebook by the improved version of SCA in the VQ compression algorithm. The advantage of the proposed method is finding optimal codebooks and increasing the quality of compressed images. The proposed method implementing in MATLAB software, and experiments showed that the proposed method's PSNR index improves the VQ algorithm's ratio by 13.73%. Evaluations show that the proposed method's PSNR index of compressed images is higher and better than PBM, CS-LBG, FA-LBG, BA-LBG, HBMO-LBG, QPSO-LBG, and PSO-LBG. The result shows that the proposed method (or ISCA-LBG) has less time complexity than HHO and WOA compression algorithms.