A BLIND IMAGE SUPER-RESOLUTION ALGORITHM FOR PURE TRANSLATIONAL MOTION Fatih Kara 1 and Cabir Vural 2 1 TUBITAK-UEKAE (National Research Institute of Electronics and Cryptology) P.K. 74, 41470, Gebze, Kocaeli, Turkey 2 Departmant of Electrical-Electronics Engineering, Sakarya University, Esentepe, Sakarya 54187, Turkey phone: + (90) 262 6481363, fax: + (90) 262 6481100, email: fkara@uekae.tubitak.gov.tr ABSTRACT In almost all super-resolution methods, the blur operator is assumed to be known. However, in practical situations this operator is not available or available only within a finite extend. In this paper, a super-resolution algorithm is presented in which the assumption of availability of the blur parameters is not necessary. It is a two-dimensional and single-input multiple-output extension of the well-known constant modulus algorithm which is widely used for blind equalization in communication systems. The algorithm consists of determining a set of deconvolution filters to be applied on interpolated low-resolution and low-quality images and is suitable for pure translational motion only and shift-invariant blur. Experimental results have shown that the proposed method can satisfactorily reconstruct the high-resolution image and remove the blur especially for five or less-bit images. 1. INTRODUCTION Super-resolution image reconstruction can be defined as the process of constructing a high-quality and high-resolution image from several shifted, degraded and undersampled ones. In areas such as medical imaging and satellite imaging, where multiple frames of the same scene can be obtained, super-resolution is proven to be useful. Also, multiple frames in a video sequence can be utilized to improve the resolution for frame-freeze or zooming purposes. In the literature, super-resolution is treated as an inverse problem, where the high-quality and high-resolution image to be obtained is linked to the undersampled images by a series of operators such as warping, blur, decimation and additive noise. Among recent work are projection onto convex sets (POCS) approach, iterative back-projection, maximum a posteriori (MAP) estimation, etc. Excellent tutorials about the subject can be found in [1] and [2]. In almost all above methods, in order for the high-resolution image to be reconstructed, the blur and the motion operators should be known in advance. Although the motion parameters are estimated a priori to some extend, as known to the authors, the blur operator is just assumed to be in hand. But this is hardly the case in practice. Either the blur parameters must be estimated or the high-resolution image must be constructed without the need for the blur parameters, hence the term blind image super-resolution. In this work, a blind super-resolution image reconstruction method is developed for pure translational motion and shift- invariant blur. Generally, the blur is modelled as a 2-D finite impulse response (FIR) filter and need not be the same for all low-resolution images. The high-resolution image is estimated by superposing the degraded images after they pass through distinct adaptive FIR reconstruction filters whose coefficients are updated by using the 2-D version of the constant modulus algorithm (CMA). CMA [3, 4] is a popular tool in the area of blind equalization in communications, where the aim is to suppress the intersymbol interference (ISI). It can also be used in single- input multiple-output (SIMO) or multiple-input multiple- output (MIMO) systems as well as in single-input single- output (SISO) systems, to reduce the interuser interference (IUI) besides ISI [5]. The idea of the CMA depends on the fact that the source is of constant modulus or from a finite alphabet. In this context, image can be considered as a finite-alphabet source because each pixel is represented by a finite (usually 8) number of bits. Vural and Sethares [6] utilized this property to develop a CMA-based blind single-image blur removal algorithm. The work presented here is essentially an extention of the mentioned algorithm to the single-input multiple-output case. The paper is organized as follows: In Section 2, the observation model that links the high-resolution image to the observed low-resolution images is presented. If the motion between the LR images consists of only pure translational motion, then the model can be simplified. Based on the simplified model, the super-resolution problem is formulated. In Section 3, the CMA-based high-resolution image reconstruction algorithm is developed. In Section 4, experimental results are presented and some conclusions are drawn in Section 5. 2. SYSTEM DESCRIPTION Figure 1 shows the observation model that links the high- resolution image to the observed low-resolution ones. In this model, the LR image is obtained by successive operations such as warping, blurring and subsampling on the high- resolution image. In general, the warp operator (denoted by W 1 , W 2 , … , W M , where M is the number of observed low- 14th European Signal Processing Conference (EUSIPCO 2006), Florence, Italy, September 4-8, 2006, copyright by EURASIP