# A Fast Method of Visually Lossless Compression of Dental Images
## 1 Introduction  
Image processing has found numerous applications in multimedia and smart education [1; 2; 3], remote sensing and non-destructive control [4; 5; 6], etc. It is widely used in various medical applications [7; 8; 9]. Medical images acquired by different types of devices are applied in diagnostics and control in numerous branches of medicine. One of them is in dentistry [10; 11], for which imaging systems and acquired images have specific peculiarities. The most modern imaging systems produce dental images of large size [12; 13]. This causes a problem for their storage if the number of daily or monthly acquired images is very large [14], and in image transmission via communication channels in telemedicine [15]. Therefore, it is desirable to use image compression to reduce data size for storing, handling and transmitting content [14; 15; 16; 17]. There are two types of image compression algorithms--lossless and lossy compression [18; 19]. It has been well understood [19; 20] that lossless (reversible) compression provides a small compression ratio (CR) that often does not meet the requirements of the storage and/or transmission of medical data; and the use of lossy compression can be, in general, acceptable in practice but only under specific conditions. The main condition is that distortions introduced by a lossy compression should not reduce a diagnostic value of an image (i.e., distortions should be \"invisible\" and/or no artifactsshould be introduced due to compression). Other conditions relate to the computation efficiency and security. Compression and decompression should be fast; sometimes standard coders have to be used [20], whilst the use of non-standard coders can provide an extra security of compressed data. The main problem in the modern lossy compression is to provide a reasonable trade-off between CR (in bitrate, bits per pixel--bpp) and image quality (characterized by a metric's value). With an application to medical images (e.g., dental images), this problem can be solved in different ways:  
1. Setting a recommended or maximal CR for the considered type of images [19; 20; 21; 22] for a given compression method. This practically guarantees invisibility of distortions but makes it impossible to adapt to image/noise properties and thus increase CR when it is possible;
2. Controlling a quality of an image subject to compression and reaching a possible limit [20]. In this case, there are two bottlenecks. One is that an adequate metric should be chosen, and the corresponding distortion invisibility threshold must be known in advance. The standard peak signal-to-noise ratio (PSNR) is known to be not always a reliable metric from a human visual system point of view, a choice of other visual quality metrics can be a question alongside threshold selection [23]. Thus, a compression can become iterative for finding a proper parameter that controls compression (PCC), for example, quality factor for JPEG, bitrate for JPEG2000 or Set partitioning in hierarchical trees (SPIHT), quantization step (QS) for discrete cosine transform (DCT)-based coders [24; 25; 26; 27], etc. Another bottleneck is that such a compression might need extensive computational and time expenses, which is undesirable. Thus, fast procedures for providing invisibility of distortions and high CR are needed. Medical images, in general, and dental images, in particular, can be corrupted by a noise [28; 29; 30], which can be seen well in the visualized data. Noise properties depend on many factors and, in general, are not purely additive and white [29; 30; 31]. Moreover, a lossy image compression had several peculiarities discovered in [32; 33] and was considered later in the literature [34; 35]. A main peculiarity is a specific noise filtering effect that appears due to a lossy compression. This effect is mostly positive but only if low contrast informative details are not removed or considerably smeared. Thus, noise properties in the case of compressing noisy images must be considered in the ooder's PCC setting.