SVD-Based Image De-nosing with the Minimum Energy Model

Abstract

This paper proposes a new solution integrating energy function into singular value decomposition (SVD) for image de-noising. The singular values on the diagonal matrix obtained through SVD represent different components in image. By selecting the proper singular values that represent signal and discarding the ones that represent noise, the additive noise of an image can be eliminated effectively. In order to obtain the optimal number of the singular values for image reconstruction and to eliminate the noise, the paper presents a minimum energy model. This model is used to obtain the optimum number for de-noising through calculating the minimum in the defined energy curve. The experiment results show that the established model is effective in the circumstance that the image has simple/regular structure/pattern.

Denoising via truncated sparse decomposition

“…The results indicate that the TSD is more efficient than NNSC [4] and SVD-based denoising algorithm. [9] The WS has the worst average performance in both experiments, thus it might be not suitable for denoising noisy chaotic signals.…”

“…Minimum energy model truncate operation Similar to the SVD-based denoising method first proposed in Ref. [9], the TSD-based denoising algorithm also depends on the accurate estimation of the value t. In recent years, variational and partial differential equation (PDE) methods have also been widely used in many applications. [10,11] There are several methods for solving a PDE and the principle behind them is to minimize energy functionality.…”

“…The first item E 1 (a) in the model presents the smoothness of data, called the smoothness energy and the second item E 2 (a) presents the disparity between the restored data and the noisy data, called the disparity energy. [9] Here we use the following calculation method:…”