The purpose of the article is to develop recommendations for choosing image compression method based on wavelet transformation, depending on image type, quality and compression requirements. Among the wavelet image compression methods, Embedded Zerotree Wavelet coder (EZW) and Set Partition In Hierarchical Trees (SPIHT) are considered, and the Haar wavelet and wavelet transformation in the oriented basis with the first, third, fifth and seventh decomposition levels is used as the base wavelet transform. These compression methods were compared with each other and with the standard JPEG method on the following parameters: mean square error, maximum error, peak to noise ratio, number of bits per pixel, compression ratio, and image size. The proposed methods can be successfully applied in the transmission of seabed relief images obtained from satellites or sea buoys.