Description

We will demonstrate three techniques of image de-noising through Singular Value Decomposition (SVD). In the first method, we will use SVD to represent a single noisy image as a linear combination of image components, which is truncated at various terms. We will then compare each image approximation and determine the effectiveness of truncating at each term. The second technique, extends the concept of image de-noising via SVD, but uses a block wise analysis to conduct de-noising. We will show that block wise SVD de-noising is the least effective at removing noise compared to our other techniques. Finally, we will discuss image de-noising with block wise Principal Component Analysis (PCA) computed through SVD. Compared to the first two techniques, this is a superior technique in reducing the image RMSE Digital images are often corrupted with noise during acquisition and transmission, degrading performance in later tasks such as: image recognition and medical diagnosis. Many denoising algorithms have been proposed to improve the accuracy of these tasks when corrupted images must be used. However, most of these methods are carefully designed only for a certain type of noise or require assumptions about the statistical properties of the corrupting noise. Classical image denoising algorithms based on single noisy images and generic image databases will soon reach their performance limits. In this paper, we propose to denoise images using targeted external image databases. Formulating denoising as an optimal filter design problem, we utilize the targeted databases to (1) determine the basic functions of the optimal filter by means of group sparsity; (2) determine the spectral coefficients of the optimal filter by means of localized priors. For a variety of scenarios such as text images, multiview images, and face images, we demonstrate superior denoising results over existing algorithms. In this paper, we propose an adaptive image denoising algorithm using a targeted external database instead of a generic database. Here, a targeted database refers to a database that contains images relevant to the noisy image only. As will be illustrated in later parts of this paper, targeted external databases could be obtained in many practical scenarios, such as text images (e.g., newspapers and documents), human faces (under certain conditions), and images captured by multiview camera systems. Other possible scenarios include images of license plates, medical CT and MRI images, and images of landmarks.