The scientific world has witnessed an explosion in the development of comprehensive and high-throughput methods for molecular biology experimentation. High-density DNA microarray technology, allows researchers to monitor the expression levels of thousands of genes in an organism simultaneously, to characterize genetic diseases at the molecular level and to direct new treatment for specific cellular aberrations. The microarray analysis is rapidly becoming a standard research tool. But, the images produced by microarray experiments, are not perfect and includes noisy sources, that contaminate them during the various stages of its formation. These microarray images need to be denoised to ensure reliable and accurate downstream analysis. A major challenge in DNA microarray analysis is to effectively dissociate actual gene expression values from experimental noise. This thesis, focuses on proposing an efficient noise reduction technique for microarray images, by using an appropriate model for the complex wavelet coefficients, obtained by decomposition of these images using a complex transform.;Among the number of filtering and enhancement techniques available for noise reduction, wavelet-based approaches have been more successful as it processes the images in multiresolution. In particular, complex wavelets have been more successful in image denoising due to its shift invariance property and improved directional selectivity. A two-channel cDNA microarray experiment generates two 16-bit red and green channel images that reflect the expression levels of the genes in treatment and control samples respectively. Since the two channel images produced are from the same microarray slide, a significant noise correlation between the microarray images exist and methods that exploit this property of inter-channel signal and noise correlation between the two channel images in the complex wavelet domain, achieve better denoising performance. The Gaussian scale mixtures (GSM) model of wavelet coefficients using Bayesian least square(BLS) estimator has been very effective in noise reduction for natural images. To fully utilize the usefulness of complex wavelet coefficients, complex Gaussian scale mixtures (CGSM) model has been developed as an extension of the GSM for real wavelet coefficients. The CGSM model of complex wavelet coefficients, improves the quality of denoised images from using the GSM of real wavelet coefficients.;In this work, we combine the advantages of using an improved CGSM model of the complex wavelet coefficients, by taking into consideration the inter-channel dependency in the complex coefficients of the image as well as the noise for denoising the red and green channel images. Thus, we propose to jointly denoise the two channel microarray images by modeling the complex coefficients of signal and noise using CGSM, by incorporating the joint statistics of the images into the model to achieve better noise reduction performance.;Extensive experimentations are carried out on a set of cDNA microarray images, to evaluate the performance of the proposed denoising methods as compared to the existing ones. Comparisons are made using standard metrics such as, the peak signal-to-noise ratio (PSNR) for measuring the amount of noise removed from the pixels of the images, and the structural similarity (SSIM) index as a measure of signal preservation quality of the denoised images to the original image. To impress the usefulness of the joint model, we have compared the joint denoising of the two channel images with independent denoising of these images using same CGSM model. We find the best window size for denoising these microarray images using our proposed method such that, the PSNR of the output images is maximized. We have also compared the performance of the our algorithm against some existing noise reduction methods in literature. We have used the Dual Tree- Complex Wavelet Transform (DT-CWT), which is probably the most widely used complex wavelet transform in image processing, but have also compared our method with other complex-valued multiresolution transforms, such as the fast discrete curvelet transform (FDCT), the pyramidal dual-tree directional filter bank (PDTDFB), and the uniform discrete curvelet transform (UDCT). Results indicate that the proposed denoising method adapted to microarray images, do indeed, lead to better noise reduction evaluated in terms of PSNR and SSIM. Thus, we expect our proposed model for noise reduction, to play a significant role in improving the reliability of the results obtained from practical microarray experiments.
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