SPLAYN USULLARI ASOSIDA TIBBIY TASVIRLARGA RAQAMLI ISHLOV BERISH

Аннотация

In modern medicine, digital image processing technologies play a crucial role in assessing human health, enabling early disease detection, and improving treatment effectiveness. In particular, the accuracy of medical images obtained through magnetic resonance imaging (MRI), computed tomography (CT), and ultrasound examinations is one of the key factors determining diagnostic precision. However, in practical applications, medical images are often degraded due to noise, lighting variations, insufficient contrast, or reduced clarity, which may lead to diagnostic errors. Therefore, digital processing of medical images, enhancing their quality, reducing noise, restoring lost data, and developing more accurate diagnostic models have become significant scientific challenges. Classical interpolation and filtering methods provide certain efficiency but are limited by computational complexity and trade-offs between smoothness and accuracy. Recently, spline-based modeling and interpolation methods have gained wide application in image processing. These methods ensure smooth and accurate reconstruction across image regions, enhancing both visual and numerical quality. In particular, bicubic spline-based models demonstrate high smoothness and stability across all image segments. This study aims to develop a medical image processing model based on spline methods, improve existing filtering and interpolation approaches, evaluate their performance, and explore their application in diagnostic systems. The proposed approach contributes to medical informatics, digital signal processing, and computer-aided diagnostics, improving the reliability of decisions directly affecting human health and well-being. 293 ResearchBib IF - 11.01, ISSN: 3030-3753, Volume 2 Issue 10 Keywords: Digital images, medical image processing, spline functions, bicubic interpolation, digital filter, hybrid algorithm, PSNR, SSIM. 2. Adabiyotlar sharhi So‘nggi yillarda splayn funksiyalarining raqamli signallar va tasvirlarni qayta ishlashdagi qo‘llanishi kengayib bormoqda. Zaynidinov H.N. (2016) tomonidan taklif etilgan polinomial splaynlar raqamli tizimlarda signallarni silliqlash, interpolatsiya qilish hamda ularning aniqligini oshirishda muhim ahamiyat kasb etadi. Ushbu yondashuv splayn asosida qurilgan modellar yordamida signallarning lokal o‘zgarishlarini aniqlash va shovqindan xoli shaklga keltirish imkonini beradi. Tibbiy tasvirlarni qayta ishlash sohasida Xodjayeva D.F. va hamkorlari tomonidan olib borilgan tadqiqotlarda sun’iy intellekt, aqlli tizimlar hamda raqamli filtrlash usullarining o‘zaro integratsiyasi masalalari keng yoritilgan. Ularning ishlarida aqlli uy tizimlarida suv haroratini boshqarish, energiya sarfini optimallashtirish va raqamli nazorat tizimlarini avtomatlashtirish bo‘yicha samarali algoritmlar ishlab chiqilgan (Hodjaeva D.F., 2023; 2024).Shuningdek, mualliflar (Zaynidinov, Hodjaeva, Xuramov, 2023) tomonidan tibbiy- biomedikal tasvirlarni raqamli qayta ishlashda to‘lqinli o‘zgartirish (wavelet) va splayn interpolatsiya usullarini birlashtirish orqali yuqori sifatli diagnostik natijalarga erishish mumkinligi isbotlangan. Ularning tadqiqotlari shuni ko‘rsatadiki, bunday gibrid yondashuv tibbiy tasvirlarning aniqligini oshiradi, shovqin darajasini kamaytiradi va tasvirdagi muhim strukturaviy elementlarni saqlab qoladi. Zaynidinov H.N. va Hodjayeva D.F. tomonidan ishlab chiqilgan energiya iste’molini boshqarish hamda fuzzy logika algoritmlari asosidagi modellarda ham splayn funksiyalarining soddaligi va hisoblash barqarorligi e’tiborga olingan. Ularning tadqiqotlari (2022–2024-yillar oralig‘ida) shuni tasdiqlaydiki, splayn funksiyalari nafaqat texnik tizimlarda, balki tibbiy tasvirlarni qayta ishlashda ham silliqlik va aniqlikni ta’minlashda samarali vosita bo‘lib xizmat qiladi. Xorijiy va mahalliy tadqiqotlar tahlili shuni ko‘rsatadiki, splayn usullarini raqamli filtratsiya bilan birlashtirish orqali tibbiy tasvirlar sifatini yaxshilash, diagnostika aniqligini oshirish va shovqinlarni kamaytirish imkoniyatlari mavjud. Shu sababli, mazkur ishda raqamli filtr va bikubik splayn interpolatsiyasini birlashtiruvchi gibrid model ishlab chiqish va uni tibbiy tasvirlarga tatbiq etish dolzarb ilmiy yo‘nalish sifatida tanlangan. 3. TADQIQOT METODOLOGIYASI 3.1. Tadqiqotning umumiy yondashuvi Tibbiy tasvirlarni qayta ishlashda asosiy maqsad — shovqinni kamaytirgan holda tasvir aniqligini oshirishdir. Buning uchun biz raqamli filtr va bikubik splayn interpolatsiya usullarini birlashtirgan gibrid modelni taklif qilamiz. Bu yondashuvda birinchi bosqichda tasvir filtrlashdan o‘tadi, ikkinchi bosqichda esa splayn asosida silliqlanadi. Natijada tasvir shovqindan tozalanadi va silliq, uzluksiz shaklda qayta tiklanadi. 3.2. Raqamli filtrlash jarayoni Filtrlash bosqichi tasvirdagi shovqinlarni yo‘qotish uchun amalga oshiriladi. Bu jarayon quyidagi umumiy tenglama bilan ifodalanadi bu yerda:  I(x,y) — kiruvchi tasvir piksellari, 294 ResearchBib IF -