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The purpose of image compression is to reduce the number of bits required to represent data by removing data redundancy. Lossless compression approaches, such as Huffman, Fano, Run Length, Arithmetic, and LZW Coding, are used to achieve compact code. The approach that can achieve compact code is regarded as close to the best solution. Lossless compression utilizes compression technologies that do not lose information, allowing compressed data to recover back to the original image without error. Common lossless compression methods include Huffman, run length, arithmetic, and Rice algorithm. The minimum amount of lossless compression data is limited by its information entropy, and the efficiency is limited. Entropy is a measure of the degree of uncertainty in a set of random variables, and it provides a criterion to measure the performance of bit-specific codes. Typical coding methods include Huffman, Fano, and Shannon encoding methods. Lossless compression is divided into two steps: de-correlation and encoding. Various lossless compression approaches are discussed, including Huffman coding, Fano coding, Run Length Coding, and Arithmetic Coding. Each method has its own advantages and disadvantages, and they are often used in combination with other coding methods to compress image data.