Stricter requirements for new satellite systems for remote sensing of the Earth (ERS) require the use of video cameras of different frequency ranges with high resolution, which leads to a significant increase in the volume of images. Applied in modern remote sensing satellites SPOT-5, IRS-P5, Beijing-1 and Cartosat-1,2 JPEG method, and on satellites IMS-1, x-SAT, PLEIADES-HR, Radarsat-2 and TerraSAR method JPEG-2000 have a number of limitations due to the fact that they were developed in the era of television standards NTSC, PAL and SECAM. It is known that the procedures of compression and decompression, protective coding and decoding are symmetrical. This is the basis for using orthogonal transformations in these procedures. The choice of DCT in these algorithms in their development was due, including, small size of personnel. However, modern practice shows that not always DCT allows you to successfully compress the image and keep it informative at a resolution of 4K, 8K or more. The explanation is simple-the size of the small parts in the high-resolution image is commensurate with the size of the DCT matrix. One of the ways to solve the problem of high-quality image processing with high resolution is the creation and use of new compression filters, new algorithms of noise-resistant coding, based on the use of orthogonal and quasi-orthogonal matrices of large sizes.