One of the most important problems in computer applications are the storage and transmission of images that makes the field of developing the image compression. For that, various compression methods have been proposed using different techniques to achieve high compression ratios and high image quality. Among these techniques are the Wavelet Transform (WT) and Transform Coding (TC) methods. In the wavelet transform method, which is the subject of this work, a wavelet transform may be used to divide the image into sub-bands. A type of wavelet transform is used here, the integer wavelet transform (IWT). The sub-band division can be repeated more than once (or the wavelet process can be of one or more passes). Then after the decomposition, the resultant wavelet coefficients are rounded to nearest integer to get the compressed form. In the second approach of the work, that is the transform coding, the image data is partitioned into blocks, and each block is transformed and then compressed. This method is studied and implemented for comparison reason. Two types of images have been used for testing the result; they are either grayscale or color images. For grayscale image, the wavelet transform method achieved 1/1 to 3/1 compression ratios depending on number of compressed bits (b), while TC method achieved 3/1 to 7/1 compression ratios. For color images the WT method achieved 1/1 to 2/1 compression ratios. While TC achieved 4/1 to 7/1, with acceptable error. The obtained Peak Signal to Noise Ratio (PSNR) is well beyond 24 dB for both methods .