Hakimjon Zaynidinov et al., International Journal of Advanced Trends in Computer Science and Engineering, 9(3), May – June 2020, 2729 - 2734 2729 Digital Image Processing with Two-Dimensional Haar Wavelets Hakimjon Zaynidinov 1 , Jonibek Juraev 2 , Umidjon Juraev 3 1 Tashkent University of Information Technologies, Uzbekistan, tet2001@rambler.ru 2 Samarkand State University, Uzbekistan, jurayevju@mail.ru 3 Department of Information Technology, Gulistan State University, Uzbekistan, pingo7520@gmail.com ABSTRACT In this article an algorithm has been developed to digitally compress an image using two-dimensional Haar wavelets, reduce its size, determine the recovery coefficients, and display a higher quality image of the processed image than the original image. It is known that one of the main problems of image compression is to find and apply an effective method that allows you to present each type of pixel (dot) in a compact form. To overcome this problem, a two-dimensional Haar wavelet modification was used, and as a result, the image was compressed to make the processed image more qualitative than the existing image. Key words: Two-dimensional Haar wavelet conversion, one-dimensional Haar wavelet conversion, image digital processing, Haar's rapid conversion algorithm, discrete signal. 1. INTRODUCTION Currently, two-dimensional Haar wavelets are used in the restoration, brightening, compression of images obtained from medical devices, in image recognition, in the analysis of various images in nature (color of the eye, radiography of the kidneys, satellite images of clouds or planets, etc. possible) is used in the study of the properties of vortex fields and in other cases [2]. One of the main disadvantages of images is the lack of pixel count (low image quality) compared to the medical apparatus, and as a result, there are various difficulties in making the necessary diagnoses on X-ray images. In order to overcome these problems, the two-dimensional Haar wavelet conversion method was used [9,10]. Two-dimensional Haar wavelet modification is obtained by applying one-dimensional Haar wavelet modification, i.e., two-dimensional modification is performed by processing rows and columns of the image into a one- dimensional modification [1]. As a result of Haar wavelet modification of two-dimensional signals, the floating points of the signals are broken, resulting in small errors. Reducing this error depends on the approximation level of the signal[14]. A new DWT-Hungarian method of watermarking a color image was proposed in [15], and a new digital image processing algorithm was considered in [16]. 2. ONE DIMENSIONAL HAAR`S FAST CHANGE ALGORITHM Depending on the classes of signals, continuous and discrete wavelet modification methods are used to process them. Haar’s one-dimensional wavelet rapid change is the simplest and basis for wavelet change [3,4,7]. Get ) ,..., , ( 2 1 n f f f f one - dimensional discrete signal. As a result of discrete wavelet modification, the processed signal is divided into two pieces of equal size [5]. One is the average value view n a or approximation of the signal, and the other is the different value view n d or detail of the signal [7]. They are represented in the following form, 2 / ,..., 3 , 2 , 1 , 2 2 1 2 N n f f a n n n     (1) here Z n a a n   }, { -formula for determining the average values. If the signal has a different value, 2 / ,..., 3 , 2 , 1 , 2 2 1 2 N n f f d n n n     (2) here ) ,..., , ( 2 / 2 1 N i d d d d  -formula for determining different values[8]. These values generate two new signals Z n a a n   }, { : one to restore the original signal and the other to restore the first signal Z n d d n   }, { , indeed [6]. n n n d a f   1 2 n n n d a f   2 (3) If we look at the example of the rapid change wavelet sound signals (Figure 1) ISSN 2278-3091 Volume 9, No.3, May - June 2020 International Journal of Advanced Trends in Computer Science and Engineering Available Online at http://www.warse.org/IJATCSE/static/pdf/file/ijatcse38932020.pdf https://doi.org/10.30534/ijatcse/2020/38932020