B. M. Salam

Efficient implementation of image interpolation as an inverse problem

This paper presents three computationally efficient solutions for the image interpolation problem which are developed in a general framework. This framework is based on dealing with the problem as an inverse problem. Based on the observation model, our objective is to obtain a high resolution image which is as close as possible to the original high resolution image subject to certain constraints. In the first solution, a linear minimum mean square error (LMMSE) approach is suggested. The necessary assumptions required to reduce the computational complexity of the LMMSE solution are presented. The sensitivity of the LMMSE solution to these assumptions is studied. In the second solution, the concept of entropy maximization of the required high resolution image a priori is used. The implementation of the suggested maximum entropy solution as a single sparse matrix inversion is presented. Finally, the well-known regularization technique used in iterative nature in image interpolation and image restoration is revisited. An efficient sectioned implementation of regularized image interpolation, which avoids the large number of iterations required in the interactive technique, is presented. In our suggested regularized solution, the computational time is linearly proportional to the dimensions of the image to be interpolated and a single matrix inversion of moderate dimensions is required. This property allows its implementation in interpolating images of any dimensions which is a great problem in iterative techniques. The effect of the choice of the regularization parameter on the suggested regularized image interpolation solution is studied. The performance of all the above-mentioned solutions is compared to traditional polynomial based interpolation techniques such as cubic O-MOMS and to iterative interpolation as well. The suitability of each solution to interpolating different images is also studied.

Optimization of image interpolation as an inverse problem using the LMMSE algorithm

In this paper, a linear minimum mean square error (LMMSE) solution to the image interpolation problem is presented. The image interpolation problem is treated as an inverse problem considering the mathematical model by which a low resolution image is obtained from a high resolution image. In the suggested LMMSE (optimum) image interpolation algorithm, three main problems are encountered and solved. The autocorrelation matrix of the high resolution image is required prior to the interpolation process. This matrix is approximated from a polynomial based interpolated image and the sensitivity of the LMMSE solution to the estimation of the autocorrelation matrix is studied. Another problem is the noise variance estimation of the low resolution image. The sensitivity of the LMMSE solution to the noise variance estimation is also studied. The third problem is the large dimension matrix inversion process required for evaluating the high resolution image. This problem is solved by approximating the matrix to be inverted by a sparse matrix. Results show that the suggested solution is superior to polynomial based image interpolation algorithms from the mean square error (MSE) point of view. It is also efficient from the computational complexity point of view.

Regularized super-resolution reconstruction of images using wavelet fusion

A regularized wavelet-based image super-resolution recon- struction approach is presented. The super-resolution image reconstruc- tion problem is an ill-posed inverse problem. Several iterative solutions have been proposed, but they are time-consuming. The suggested ap- proach avoids the computational complexity limitations of existing solu- tions. It is based on breaking the problem into four consecutive steps: a registration step, a multichannel regularized restoration step, a wavelet- based image fusion and denoising step, and finally a regularized image interpolation step. The objective of the wavelet fusion step is to integrate all of the data obtained from the multichannel restoration step into a single image. The wavelet denoising is performed for the low-SNR cases to reduce the noise effect. The obtained image is then interpolated using a regularized interpolation scheme. The paper explains the implementa- tion of each of these steps. The results indicate that the proposed ap- proach has succeeded in obtaining a high-resolution image from multiple degraded observations with a high peak SNR. The performance of the proposed approach is also investigated for degraded observations with different SNRs. The proposed approach can be implemented for large- dimension low-resolution images, which is not possible in most pub- lished iterative solutions.

WAVELET FUSION: A TOOL TO BREAK THE LIMITS ON LMMSE IMAGE SUPER-RESOLUTION

This paper presents a wavelet-based computationally efficient implementation of the Linear Minimum Mean Square Error (LMMSE) algorithm in image super-resolution. The image super-resolution reconstruction problem is well-known to be an ill-posed inverse problem of large dimensions. The LMMSE estimator to be implemented in the image super-resolution reconstruction problem requires an inversion of a very large dimension matrix, which is practically impossible. Our suggested implementation is based on breaking the problem into four consecutive steps, a registration step, a multi-channel LMMSE restoration step, a wavelet-based image fusion step and an LMMSE image interpolation step. The objective of the wavelet fusion step is to integrate the data obtained from each observation into a single image, which is then interpolated to give a high-resolution image. The paper explains the implementation of each step. The proposed implementation has succeeded in obtaining a high-resolution image from multiple degraded observations with a high PSNR. The computation time of the suggested implementation is small when compared to traditional iterative image super-resolution algorithms.

A NEW APPROACH FOR ADAPTIVE POLYNOMIAL BASED IMAGE INTERPOLATION

In this paper, an adaptive algorithm is suggested for the implementation of polynomial based image interpolation techniques such as Bilinear, Bicubic, Cubic Spline and Cubic O-MOMS. This algorithm is based on the minimization of the squared estimation error at each pixel in the interpolated image by adaptively estimating the distance of the pixel to be estimated from its neighbors. The adaptation process at each pixel is performed iteratively to yield the best estimate of this pixel value. This adaptive interpolation algorithm takes into consideration the mathematical model by which a low resolution (LR) image is obtained from a high resolution (HR) image. This adaptive algorithm is compared to traditional polynomial based interpolation techniques and to the warped distance interpolation techniques. The performance of this algorithm is also compared to the performance of other algorithms used in commercial interpolation softwares such as the ACDSee and the Photopro programs. Results show that the suggested adaptive algorithm is superior from the Peak Signal to Noise Ratio (PSNR) point of view to other traditional techniques and it has a higher ability of edge preservation than traditional image techniques. The computational cost of the adaptive algorithm is studied and found to be moderate.

Blind multichannel reconstruction of high-resolution images using wavelet fusion

We developed an approach to the blind multichannel reconstruction of high-resolution images. This approach is based on breaking the image reconstruction problem into three consecutive steps: a blind multichannel restoration, a wavelet-based image fusion, and a maximum entropy image interpolation. The blind restoration step depends on estimating the two-dimensional (2-D) greatest common divisor (GCD) between each observation and a combinational image generated by a weighted averaging process of the available observations. The purpose of generating this combinational image is to get a new image with a higher signal-to-noise ratio and a blurring operator that is a coprime with all the blurring operators of the available observations. The 2-D GCD is then estimated between the new image and each observation, and thus the effect of noise on the estimation process is reduced. The multiple outputs of the restoration step are then applied to the image fusion step, which is based on wavelets. The objective of this step is to integrate the data obtained from each observation into a single image, which is then interpolated to give an enhanced resolution image. A maximum entropy algorithm is derived and used in interpolating the resulting image from the fusion step. Results show that the suggested blind image reconstruction approach succeeds in estimating a high-resolution image from noisy blurred observations in the case of relatively coprime unknown blurring operators. The required computation time of the suggested approach is moderate.

ADAPTIVE LEAST SQUARES ACQUISITION OF HIGH RESOLUTION IMAGES

This paper presents a least squares block by block adaptive approach for the acquisition of high resolution (HR) images from available (LR) images. The suggested algorithm is based on the segmentation of the image to overlapping blocks and the interpolation of each block separately. The purpose of the overlapping of blocks is to avoid edge effects. An adaptive 2D least squares approach, which considers the image acquisition model, is used in the minimization of the estimation error of each block. In this suggested algorithm, a weight matrix of moderate dimensions is estimated in a small number of iterations to interpolate each block. This algorithm avoids the large computational complexity due to the matrices of large dimensions required to interpolate the image as a whole. The performance of the proposed algorithm is studied for different LR images with different SNRs. The performance of the proposed algorithm is also compared to the standard as well as the warped distance cubic O-MOMS image interpolation algorithms from the PSNR point of view.

NEW TECHNIQUES TO CONQUER THE IMAGE RESOLUTION ENHANCEMENT PROBLEM

This paper presents some new techniques for high resolution (HR) image processing and compares between them. The paper focuses on two main topics, image interpolation and image super- resolution. By image interpolation, we mean extracting an HR image from a single Degraded low resolution (LR) image. Polynomial based image interpolation is reviewed. Some new techniques for adaptive image interpolation and inverse image interpolation are presented. The other topic treated in this paper is image super-resolution. By image super resolution, we mean extracting a single HR image either from multiple observations or multiple frames. The paper focuses on the problem of image super resolution using wavelet fusion and presents several super resolution reconstruction algorithms based on the idea of wavelet fusion.

A greatest common divisor approach to blind super-resolution reconstruction of images

An algorithm for blind super-resolution reconstruction of a single image from multiple degraded observations is developed. The algorithm depends on estimating the 2D greatest common divisor (GCD) between each observation and a combinational image generated by a weighted averaging process of the available observations. The purpose of generating this combinational image is to obtain a new image with a higher signal to noise ratio, and a blurring operator that is co-prime with all the blurring operators of the available observations. The 2D GCD is then estimated between the new image and each observation and thus the effect of noise on the estimation process is reduced. The results of each 2D GCD process are fused to form a single reconstructed image, which is then interpolated subject to local regularization to form a high-resolution (HR) image. Results show that the proposed algorithm succeeds in estimating an HR image from noisy blurred observations in the case of relatively co-prime unknown blurring operators.

A SIMPLE ADAPTIVE INTERPOLATION APPROACH BASED ON VARYING IMAGE LOCAL ACTIVITY LEVELS

In this paper, a simple adaptive interpolation approach is proposed for image interpolation. It depends on modifying the warped distance technique for image interpolation considering the local activity levels in each region of the image. This is performed by weighting the pixels used in the interpolation process with different adaptive weights. The adaptation can be extended to different traditional interpolation techniques such as bilinear, bicubic and cubic spline techniques as well as the warped distance technique. Our study shows that the adaptive weighting of pixels in interpolation yields better results than that obtained using only traditional interpolation methods or by using the warped distance technique. The computation cost of the suggested interpolation approach is moderate and acceptable.