GRADIENT DESCENT METHOD AND PARAMETER SELECTION FOR IMAGE RESTORATION PROBLEM

Image enhancement is a meaningful problem in many practical applications. It plays an important role in preprocessing steps for recognition and information extraction. Image restoration is often considered one of the data processing steps before the training process for machine learning models is performed. Image restoration problems are often solved by iterative algorithms, where the choice of iteration parameters plays an important role in improving the algorithm's convergence rate. The problem is determining the parameters that ensure the algorithm has the fastest convergence rate. In this paper, we propose a parameter selection method for the Gradient descent algorithm to recover the original image data from the image obtained after performing morphological transformation on the original image. According to this method, we analyze the eigenvalues of the morphological transformation matrix to derive a formula to determine the optimal parameters for the Gradient descent algorithm. We have proven that the iterative process converges from the parameter determination formula. The experimental results also show that the proposed theory is consistent and confirms that the approximate solution converges to the solution of the original problem. Keywords: Image restoration; Gradient descent; iterative method; convex optimization; optimal parameter.