Image compression is one of the data compression types applied to digital images in order to reduce their high cost for storage and/or transmission. Image compression algorithms may take the benefit of visual sensitivity and statistical properties of image data to deliver superior results in comparison with generic data compression schemes, which are used for other digital data. In the first approach, the input image is divided into blocks, each of which is 16 x 16, 32 x 32, or 64 x 64 pixels. The blocks are converted first into a string; then, encoded by using a lossless and dictionary-based algorithm known as arithmetic coding. The more occurrence of the pixels values is codded in few bits compare with pixel values of less occurrence through the sub intervals between the range 0 and 1. Finally, the stream of compressed tables is reassembled for decompressing (image restoration). The results showed a compression gain of 10-12% and less time consumption when applying this type of coding to each block rather than the entire image. To improve the compression ratio, the second approach was used based on the YCbCr colour model. In this regard, images were decomposed into four sub-bands (low-low, high-low, low-high, and high-high) by using the discrete wavelet transform compression algorithm. Then, the low-low sub-band was transmuted to frequency components (low and high) via discrete wavelet transform. Next, these components were quantized by using scalar quantization and then scanning in a zigzag way. The compression ratio result is 15.1 to 27.5 for magnetic resonance imaging with a different peak signal to noise ratio and mean square error; 25 to 43 for X-ray images; 32 to 46 for computed tomography scan images; and 19 to 36 for magnetic resonance imaging brain images. The second approach showed an improved compression scheme compared to the first approach considering compression ratio, peak signal to noise ratio, and mean square error.