title: Ð¡Ð¶Ð°ÑÐ¸Ðµ Ð¸Ð½ÑÐ¾ÑÐ¼Ð°ÑÐ¸Ð¸ Ð½Ð° Ð¾ÑÐ½Ð¾Ð²Ðµ Ð²ÐµÐ¹Ð²Ð»ÐµÑ Ð¿ÑÐµÐ¾Ð±ÑÐ°Ð·Ð¾Ð²Ð°Ð½Ð¸Ð¹
title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð±Ð°ÐºÐ°Ð»Ð°Ð²ÑÐ°
titleType: Subtitle
title: Information compression based on wavelet transformations
Creators: name: ÐÐµÑÑÐ¾Ð², ÐÐ½Ð´ÑÐµÐ¹
Publisher: name: Ð¡Ð°Ð½ÐºÑ-ÐÐµÑÐµÑÐ±ÑÑÐ³ÑÐºÐ¸Ð¹ Ð¿Ð¾Ð»Ð¸ÑÐµÑÐ½Ð¸ÑÐµÑÐºÐ¸Ð¹ ÑÐ½Ð¸Ð²ÐµÑÑÐ¸ÑÐµÑ ÐÐµÑÑÐ° ÐÐµÐ»Ð¸ÐºÐ¾Ð³Ð¾
Year: 2023
Subjects: Ð¸Ð½ÑÐ¾ÑÐ¼Ð°ÑÐ¸Ñ
Ð²ÐµÐ¹Ð²Ð»ÐµÑ-Ð¿ÑÐµÐ¾Ð±ÑÐ°Ð·Ð¾Ð²Ð°Ð½Ð¸Ðµ
ÑÐ¶Ð°ÑÐ¸Ðµ Ð´Ð°Ð½Ð½ÑÑ
information
wavelet transform
data compression

description: Ð¢ÐµÐ¼Ð° ÑÐ°Ð±Ð¾ÑÑ: ÑÐ¶Ð°ÑÐ¸Ðµ Ð¸Ð½ÑÐ¾ÑÐ¼Ð°ÑÐ¸Ð¸ Ð½Ð° Ð¾ÑÐ½Ð¾Ð²Ðµ Ð²ÐµÐ¹Ð²Ð»ÐµÑ-Ð¿ÑÐµÐ¾Ð±ÑÐ°Ð·Ð¾Ð²Ð°Ð½Ð¸Ð¹.ÐÑÐµÐ´Ð¼ÐµÑ ÑÐ°Ð±Ð¾ÑÑ: ÑÐ¶Ð°ÑÐ¸Ðµ Ð¸Ð½ÑÐ¾ÑÐ¼Ð°ÑÐ¸Ð¸ Ð½Ð° Ð¾ÑÐ½Ð¾Ð²Ðµ Ð²ÐµÐ¹Ð²Ð»ÐµÑ-Ð¿ÑÐµÐ¾Ð±ÑÐ°Ð·Ð¾Ð²Ð°Ð½Ð¸Ð¹.Ð¦ÐµÐ»Ñ ÑÐ°Ð±Ð¾ÑÑ: Ð¿ÑÐ¾Ð²ÐµÑÑÐ¸ Ð°Ð½Ð°Ð»Ð¸Ð· ÑÐ¶Ð°ÑÐ¸Ñ Ð¸Ð½ÑÐ¾ÑÐ¼Ð°ÑÐ¸Ð¸ Ð½Ð° Ð¾ÑÐ½Ð¾Ð²Ðµ Ð²ÐµÐ¹Ð²Ð»ÐµÑ-Ð¿ÑÐµÐ¾Ð±ÑÐ°Ð·Ð¾Ð²Ð°Ð½Ð¸Ð¹ Ð¸ ÑÑÐ¾ÑÐ¼Ð¸ÑÐ¾Ð²Ð°ÑÑ Ð¼ÐµÑÑ Ð¿Ð¾ ÐµÐµ Ð¾Ð¿ÑÐ¸Ð¼Ð¸Ð·Ð°ÑÐ¸Ð¸.ÐÐµÑÐ¾Ð´Ð¾Ð»Ð¾Ð³Ð¸Ñ: ÑÐµÐ¾ÑÐµÑÐ¸ÑÐµÑÐºÐ¾Ðµ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ðµ Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼Ð¾Ð² Ð²ÐµÐ¹Ð²Ð»ÐµÑ-Ð¿ÑÐµÐ¾Ð±ÑÐ°Ð·Ð¾Ð²Ð°Ð½Ð¸Ð¹, Ð¿ÑÐ°ÐºÑÐ¸ÑÐµÑÐºÐ°Ñ ÑÐµÐ°Ð»Ð¸Ð·Ð°ÑÐ¸Ñ Ð² Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ð½Ð¾Ð¹ ÑÑÐµÐ´Ðµ Ð¿ÑÐµÐ´Ð»Ð¾Ð¶ÐµÐ½Ð½Ð¾Ð¹ Ð¼ÐµÑÐ¾Ð´Ð¸ÐºÐ¸.Ð ÐµÐ·ÑÐ»ÑÑÐ°ÑÑ ÐÐÐ : ÐÐ¾ÑÑÐ°Ð²Ð»ÐµÐ½Ð½ÑÐµ Ð² ÑÐ°Ð±Ð¾ÑÐµ Ð·Ð°Ð´Ð°ÑÐ¸ ÑÐµÑÐ°Ð»Ð¸ÑÑ Ð¿ÑÐ¸Ð¼ÐµÐ½ÐµÐ½Ð¸ÐµÐ¼ Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼Ð¾Ð² ÐÐÐ Ð¥Ð°Ð°ÑÐ°, ÐÐ¾Ð±ÐµÑÐ¸ Ð¸ ÐÐÐ Ð² ÐÐ Ð´Ð»Ñ ÑÐ¶Ð°ÑÐ¸Ñ ÑÐ¸ÑÑÐ¾Ð²ÑÑ Ð¸Ð·Ð¾Ð±ÑÐ°Ð¶ÐµÐ½Ð¸Ð¹. ÐÑÐµÐ½ÐºÐ° ÐºÐ°ÑÐµÑÑÐ²Ð° ÑÐ¶Ð°ÑÑÑ Ð¸Ð·Ð¾Ð±ÑÐ°Ð¶ÐµÐ½Ð¸Ð¹ Ð¿Ð¾ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ñ Ñ Ð¸Ñ Ð¾ÑÐ¸Ð³Ð¸Ð½Ð°Ð»Ð°Ð¼Ð¸ Ð²ÑÐ¿Ð¾Ð»Ð½ÑÐ»Ð¾ÑÑ Ð·Ð° ÑÑÐµÑ Ð¾ÑÐµÐ½ÐºÐ¸ ÑÑÐµÐ´Ð½ÐµÐºÐ²Ð°Ð´ÑÐ°ÑÐ¸ÑÐµÑÐºÐ¾Ð³Ð¾ Ð¾ÑÐºÐ»Ð¾Ð½ÐµÐ½Ð¸Ñ. Ð¢Ð°ÐºÐ¶Ðµ Ñ ÑÐ¾Ð¹ Ð¶Ðµ ÑÐµÐ»ÑÑ Ð²ÑÑÐ¸ÑÐ»ÑÐ»Ð¾ÑÑ ÑÑÐµÐ´Ð½ÐµÐ°ÑÐ¸ÑÐ¼ÐµÑÐ¸ÑÐµÑÐºÐ¾Ðµ Ð·Ð½Ð°ÑÐµÐ½Ð¸Ðµ Ð¿Ð¾Ð»ÑÑÐµÐ½Ð½ÑÑ Ð¿Ð¾Ð³ÑÐµÑÐ½Ð¾ÑÑÐµÐ¹ Ð¸ Ð¼Ð°ÐºÑÐ¸Ð¼Ð°Ð»ÑÐ½Ð¾Ðµ Ð¾ÑÐºÐ»Ð¾Ð½ÐµÐ½Ð¸Ðµ Ð¾Ñ Ð¾ÑÐ¸Ð³Ð¸Ð½Ð°Ð»Ð°.ÐÐ±Ð»Ð°ÑÑÑ Ð¿ÑÐ¸Ð¼ÐµÐ½ÐµÐ½Ð¸Ñ ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐ¾Ð² ÐÐÐ : ÑÐ°Ð±Ð¾ÑÐ° Ñ Ð¸Ð·Ð¾Ð±ÑÐ°Ð¶ÐµÐ½Ð¸ÐµÐ¼ Ð² ÑÐ°Ð·Ð»Ð¸ÑÐ½ÑÑ Ð¾ÑÑÐ°ÑÐ»ÑÑ Ð½Ð°ÑÐºÐ¸ Ð¸ ÑÐµÑÐ½Ð¸ÐºÐ¸, Ð¼ÐµÐ´Ð¸ÑÐ¸Ð½Ñ, ÐºÐ¾ÑÐ¼Ð¾Ð»Ð¾Ð³Ð¸Ð¸ Ð¸ Ð´Ñ.ÐÑÐ²Ð¾Ð´Ñ: ÐÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ Ð¸ ÑÑÐ°Ð²Ð½Ð¸ÑÐµÐ»ÑÐ½ÑÐ¹ Ð°Ð½Ð°Ð»Ð¸Ð· Ð¼ÐµÑÐ¾Ð´Ð¾Ð² ÑÐ¶Ð°ÑÐ¸Ñ Ð¸Ð·Ð¾Ð±ÑÐ°Ð¶ÐµÐ½Ð¸Ð¹ Ð½Ð° Ð¾ÑÐ½Ð¾Ð²Ðµ Ð´Ð¸ÑÐºÑÐµÑÐ½Ð¾Ð³Ð¾ Ð²ÐµÐ¹Ð²Ð»ÐµÑÐ° Ð¥Ð°Ð°ÑÐ° Ð¸ Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼Ð° JPEG Ð¿Ð¾Ð·Ð²Ð¾Ð»Ð¸Ð»Ð¸ ÑÑÐ¾ÑÐ¼ÑÐ»Ð¸ÑÐ¾Ð²Ð°ÑÑ ÑÐµÐºÐ¾Ð¼ÐµÐ½Ð´Ð°ÑÐ¸Ð¸ Ð¿Ð¾ Ð²ÑÐ±Ð¾ÑÑ Ð¼ÐµÑÐ¾Ð´Ð° Ð¸ ÑÑÐ¾Ð²Ð½Ñ Ð²ÐµÐ¹Ð²Ð»ÐµÑ-ÑÐ°Ð·Ð»Ð¾Ð¶ÐµÐ½Ð¸Ñ Ð² Ð·Ð°Ð²Ð¸ÑÐ¸Ð¼Ð¾ÑÑÐ¸ Ð¾Ñ Ð¶ÐµÐ»Ð°ÐµÐ¼Ð¾Ð³Ð¾ ÐºÐ°ÑÐµÑÑÐ²Ð° Ð¸ ÑÑÐ»Ð¾Ð²Ð¸Ð¹ Ð·Ð°Ð´Ð°ÑÐ¸.
description: Topic of the paper: Information compression based on wavelet transformations.Subject of the work: information compression based on wavelet transformations.The purpose of the work: to analyze the compression of information based on wavelet transformations and to form measures for its optimization.Methodology: theoretical study of algorithms of wavelet transformations, practical implementation of the proposed methodology in the software environment.The results of the WRC: The tasks set in the work were solved by using the algorithms of Haar, Dobeshi and FIBERBOARD in OB to compress digital images. The quality of compressed images compared to their originals was evaluated by estimating the mean square deviation. Also, for the same purpose, the arithmetic mean of the errors obtained and the maximum deviation from the original were calculated.The scope of application of the results of the WRC: image work in various branches of science and technology, medicine, cosmology, etc.Conclusions: Research and comparative analysis of image compression methods based on discrete Haar wavelet and JPEG algorithm allowed us to formulate recommendations on the choice of the method and the level of wavelet decomposition depending on the desired quality and conditions of the problem.