This bachelor´s thesis describes issues of wavelet compression, which is today already in common use mainly at work with digital photographs or other pictures. Saving of space regarding sizes of files is the main reason of that. There are main image formats and types of compression suitable for editing pictures desribed in this thesis. In case of lossy image compression, distortion occurs and blocking artefacts can be created. It is unwanted effect that´s why it is neccesary to use suitable data stream, compression´s rate or coding type. So the focus is on discrete wavelet transform, which uses so-called wavelets and the Haar´s wavelet is the best known of all. Next chapter of this work explores colour spaces, in which can be a picture disp...