Total variation blind deconvolution

TLDR

The TV norm is highly effective for recovering image edges and certain blur types such as motion and out‑of‑focus blur. The paper proposes a blind deconvolution algorithm that uses total variation minimization. The algorithm employs an alternating minimization implicit iterative scheme based on TV minimization to recover the image and simultaneously identify the point spread function. Numerical experiments demonstrate the scheme is robust, converges rapidly (especially for discontinuous blur), accurately recovers both image and psf under high noise, and can also identify blur kernels without sharp edges such as Gaussian blur.

Abstract

In this paper, we present a blind deconvolution algorithm based on the total variational (TV) minimization method proposed. The motivation for regularizing with the TV norm is that it is extremely effective for recovering edges of images as well as some blurring functions, e.g., motion blur and out-of-focus blur. An alternating minimization (AM)implicit iterative scheme is devised to recover the image and simultaneously identify the point spread function (psf). Numerical results indicate that the iterative scheme is quite robust, converges very fast (especially for discontinuous blur), and both the image and the psf can be recovered under the presence of high noise level. Finally, we remark that psf's without sharp edges, e.g., Gaussian blur, can also be identified through the TV approach.