Image Deblurring in Super-resolution Framework Srimanta Mandal School of Computing and Electrical Engineering Indian Institute of Technology Mandi, India Email: in.srimanta.mandal@ieee.org Anil Kumar Sao School of Computing and Electrical Engineering Indian Institute of Technology Mandi, India Email: anil@iitmandi.ac.in Abstract—In all image processing applications, it is important to extract the appropriate information from an image. But often the captured image is not clear enough to give the required information due to the imaging environment. Thus, it is essential to enhance the clarity of the image by some post-processing techniques. Image deblurring is one of such techniques to remove the blurry effect of the captured image. This paper looks into this problem in a different way, where the deblurring of an image is addressed by solving image super-resolution problem. The blurred image is first down-sampled and then it is fed to the super-resolution framework to produce the deblurred high resolution image. In addition, the proposed approach states the requirement of edge preservation in the problem. The experi- mental results are comparable with the existing image deblurring algorithms. I. Introduction Several image processing applications like medical imag- ing, surveillance etc. need good quality of image for appro- priate information extraction. But often this purpose can’t be achieved due to the limitations of the imaging ambience (lens focus, size of imaging sensor, image capturing environment etc.). As a result the captured image is sometimes blurry, which is a problem and can be described mathematically as y = Hx + z, (1) where the blurred image y ∈ R a is captured during imaging with approximated blur operator H ∈ R a×a and noise z ∈ R a . Image deblurring seeks to recover the original scene x ∈ R a from the blurry-noisy image y. In other words x needs to be deconvoluted from the blur kernel H to remove the blur, as blurry image is assumed to be produced by convolving the blur kernel with the original scene. Thus the image deblurring problem is also known as blur deconvolution and is addressed in different ways in the literature. All these works can be broadly classified into two categories: i) blind deconvolution of blur kernel [1], [2] and ii) non-blind deconvolution of blur kernel [3], [4]. The approaches belong to the first class doesn’t require any prior knowledge about the blur type, which is related to the real scenario. But the performance of these approaches mostly depend on the estimation of blur parameter from the given image which is difficult to estimate. Thus, when the blur type is given a priori due to known imaging environment, the second type of deconvolution is useful and proposed approach belongs to this category. In this paper, the deblurring/blur deconvolution problem is addressed by solving image super-resolution (SR) problem, where a down-sampled low resolution (LR) image is super- resolved to a high resolution (HR) image. The motivation behind the different perspective of viewing the deblurring problem can be justified using the super-resolution framework (see Fig. 1), where sub-pixel shifted LR images are fed to the SR system to produce a HR image [5]. If we look into the SR system, we can observe that the third block is deblurring and noise-removal, which is our main task here. So, multiple LR images produced from multiple blurred images can act as input to the SR system. But multiple blurred images of the target scene are difficult to obtain, such that the generated LR images are related to each other by sub-pixel precision. This issue can be addressed by some SR approaches, where a single LR image is required as input [6]–[9] to produce the required HR image. Thus, if the down-sampled version of the blurred image can be fed to the single image SR system, the deblurring problem can be solved. Image super-resolution is an ill-posed problem, as many HR images can produce the same LR image. Thus some regularization techniques are required to make the problem well-posed. Several regularization techniques are available in the literature [10]–[12]. In current scenario, sparse domain regularization is producing better results due to its efficient capability of signal representation under certain condition. We have used the sparse domain representation to solve the stated problem. In addition, an edge preserving constraint is added to the problem as edge information is perceptually significant [9]. Experimental results show that the proposed SR framework for solving deblurring problem is comparable with the existing deblurring approaches. The rest of the paper is organized as follows: Section II explains the sparse domain framework required for solving the deblurring problem. Section III maps the deblurring problem as SR problem. The experimental results are given in section IV and the paper is concluded in section V. II. Image deblurring using sparse domain representation In sparse domain representation, a signal x can be repre- sented as a linear combination of few columns of a dictionary matrix A ∈ R a×α (α> a) with the help of a vector c ∈ R α , whose most of the elements are zero or close to zero [13]. Mathematically it can be written as: x = Ac. (2) Thus the deblurring model as stated in (1) become y = HAc + z, (3) and can be solved with sparsity constraint as ˆ c = arg min c ||c|| 0 s.t. ||y - HAc|| 2 2 ≤ ǫ, (4)