Abstract -This paper presents a generic pattern learning based image restoration scheme for degraded digital images, where a feed-forward neural network is employed for implementation of the proposed techniques. The methodology reported in this paper can be applied in different circumstances, for instance, quality enhancement as a post-processing of image compression schemes, blur image restoration and noise image filter, provided that the training data set is comprised of patterns rich enough for supervised learning, This paper focuses on the problem of coded image restoration. The key points addressed in this work are (1) the use of edge information extracted from source images as a priori knowledge in the regularization function to recover the details and reduce the ringing artifact of the coded images; (2) the theoretic basis of the pattern learning-based approach using implicit function theorem; (3) subjective quality enhancement with the use of an image similarity for training neural networks; and (4) empirical studies with comparisons to the set partitioning in hierarchical tree (SPIHT) method. The main merits of this model-based neural image restoration approach include strong robustness with respect to transmission noise and the parallel processing for real-time applications. The experimental results demonstrate promising performance on both objective and subjective quality for lower compression ratio subband coded images. I. INTRODUCTION A degraded image may be caused by various factors such as atmospheric turbulence, distortions in the optical imaging system, lack of focus, sensor or transmission noise injection, coding techniques, and object or camera motion. The task of image restoration is to remove these degradations to enhance the quality of the image for further use in domain applications. Image restoration can be defined as a problem of estimating a source image from its degraded version. In the past, to solve this fundamental and important issue for image processing, considerable studies have been carried out using transform related techniques and algebraic approaches. The techniques involving an iterative method to minimize a degradation measure attracted many researchers and recently different models and approaches were developed such as maximum likelihood, constrained least square error and Kalman filter (see the references in [3], [10], [11]). To implement the minimization tasks for image restoration, however, we should take into account several practical factors, such as real-time requirement, or even many of the numerical optimization techniques can be used. Artificial neural networks, or simple neural networks, can be defined as a massively parallel and distributed processor that has a natural propensity for storing and recalling experiential knowledge [4], [5]. As potential tools, neural networks have been successfully applied in image processing mainly due to the ability to generate and recall an internal data representation through pattern samples learning [6],[7],[8],[9]. Some encouraging results on image restoration using neural networks have been reported in literatures [10],[11],[12]. So far, almost all of the related work used Hopfield network to find a stable point as the solution for a constrained least square error measure with a regularization term, which plays an important role in controlling the quality of restored image. If the regularization term is weighted too weaker in the error measure, the resultant restored image will contain noise artifacts. On the other hand, if the regularization measure is weighted too strongly in the error measure, the resultant restored image will be bluffed [2],[3]. Several approaches have been developed to adaptively vary the regularization parameter to achieve the optimal balance between removing edge ringing effects and suppressing noise amplification [10]. [13] presented an image restoration technique using neural networks, where a priori knowledge of the image dependent edge information was incorporated into the regularized error measure to improve the upper bound estimation of the high frequency content. A multiplayer perceptron model with single hidden layer architecture and a standard error back- propagation algorithm was employed. Although the results reported in [13] are interesting and promising, there are still some points to be emphasized and further studied. These include a proper statement of the Theorem, a modification of the cost function used for training neural networks based similarity learning, and a generalization of restoration model coded images. This paper aims at developing a pattern learning based neural image restoration technique for generic coded images. The edge information as the a priori knowledge about the source image to recover the details as well as to reduce the ringing artifact of the coded image is introduced in the regularization model to enhance the restoration performance both objectively and subjectively. A nonlinear relationship with some uncertainties among the restored image, degraded image and the edge information extracted from the source image is derived from the normal equation. It has been proved that a solution for restored image exists which is unique to certain classes of images, for given degraded image and edge information. To improve the subjective performance, an image similarity measure is applied for updating weights in neural networks. The remainder of the paper is organized as follows. Section II develops a generic image restoration model for coded images and establishes a mathematical basis for the proposed approach. Section III gives a detailed description of Pattern Learning Based Image Restoration Using Neural Networks Dianhui Wang + , Tharam Dillon + and Elizabeth Chang * + Department of Computer Science and Computer Engineering La Trobe University, Melbourne, VIC 3083, Australia * Department of Computer Science and Software Engineering Newcastle University, Australia 0-7803-7278-6/02/$10.00 ©2002 IEEE