Partial differential equation-based digital image compression models Tudor Barbu Abstract. The state of the art partial differential equation (PDE)-based image compression techniques are surveyed in this research article. An overview of the image coding approaches is described first. Next, the most important PDE-based models used in the decompression stage are presented here. Thus, image decompression schemes based on linear ho- mogeneous diffusion of various orders, nonlinear anisotropic diffusion and edge-enhancing diffusion (EED), and using encoding algorithms such as B-tree triangular coding (BTTC), rectangular subdivision or edge-based coding for image sparsification are discussed in this survey. Also, our own contributions in this domain, representing effective compression and decompression solutions using PDE-based edge detection and nonlinear anisotropic diffusion-based inpainting, are described in this paper and compared with the state of the art techniques. M.S.C. 2010: 35Kxx, 60G35, 65L12, 68U10, 68Pxx, 68P30, 68Txx, 94A08. Key words: image compression; coding algorithms; image sparsification; partial dif- ferential equations; linear homogeneous diffusion; nonlinear diffusion models; PDE- based inpainting; edge-enhancing diffusion; numerical approximation scheme. 1 Introduction Digital image compression represents an important sub-domain of both the image processing and data compression fields. The purpose of a compression task is to reduce the size of the image file without losing much information and maintaining its visual quality, in order to facilitate the storage and transmission processes. The image content is encoded using fewer bits than its original representation, in the compression process that can be either lossless or lossy [14]. The lossless image compression methods remove or reduce the statistical redun- dancy, and recover perfectly the image at decompression, no information being lost. The following coding algorithms are used for lossless compression: the Huffman co- ding, Aritmetic coding. Run Length Encoding (RLE), LZW encoding and Area coding [7, 14, 24]. Several image formats, like BMP, GIF or PNG are based on the lossless compression. Applied Sciences, Vol. 22, 2020, pp. 17-32. c ⃝ Balkan Society of Geometers, Geometry Balkan Press 2020.