M.M. Hadhoud

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.

Adaptive image interpolation based on local activity levels

In this paper, an adaptive warped distance method is suggested for image interpolation. This method depends on modifying the warped distance technique for image interpolation taking into consideration the level of activity in local regions 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 to the warped distance technique. Results show that the adaptive weighting of pixels in interpolation gives better results than that obtained using traditional interpolation methods only or by using the warped distance technique.

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.

PERFORMANCE EVALUATION OF BLOCK BASED SVD IMAGE WATERMARKING

This paper presents a block based digital image watermarking algorithm that is dependent on the mathematical technique of singular value decomposition (SVD). Traditional SVD watermarking already exists for watermark embedding on the image as a whole. In the proposed approach, the original image is divided into blocks, and then the watermark is embedded in the singular values (SVs) of each block, separately. The watermark embedding on a blockby-block basis makes the watermark more robust to the attacks such as noise, compression, cropping and lowpass filtering as the results reveal. The watermark detection is implemented by extracting the watermark from the SVs of the watermarked blocks. Extracting the watermark from one block at least is enough to ensure the existence of the watermark.

A new edge preserving pixel-by-pixel (PBP) cubic image interpolation approach

A new pixel-by-pixel (PBP) cubic image interpolation algorithm that preserves image edges is suggested in this paper. The PBP approach is based on optimizing the standard cubic image interpolation formula at each estimated pixel. Thus, the mean square error (MSE) in the entire image is minimized. A study of the effect of optimizing the cubic image interpolation formula with respect to the separated or combined parameters of the formula is presented The optimum values of the parameters are estimated iteratively at each pixel. The performance of the suggested approach is tested in the presence of different noise levels and is compared with the traditional warped distance adaptive image interpolation technique. The obtained results proves the superiority of the suggested PBP cubic image interpolation algorithm as compared to the traditional algorithm from both of the MSE and edge preservation points of view.

A simplified fractal image compression algorithm

This paper proposes a simplified fractal image compression algorithm which is implemented on a block by block basis. This algorithm achieves a compression ratio of up to 10 with a peak signal to noise ratio (PSNR) as high as 35 dB. The idea of the proposed algorithm is based on the segmentation of the image, first, into blocks to setup reference blocks. The image is then decomposed again into block ranges and a search process is carried out to find the reference blocks with best match. The transmitted or stored values, after compression, are the reference block values and the indices of the reference block that achieves the best match. If there is no match, the average value of the block range is transmitted or stored instead. The advantages of the proposed algorithm are the simplicity of computation and the high PSNR achieved.

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.

A comparison study between spiral and traditional fractal image compression

In this paper, we study the affect of using the spiral architecture instead of the square block decomposition and in fractal compression. Comparisons with other systems like the conventional square and the simplified fractal compression systems are presented. A comparison with standard JPEG system is also introduced. We applied these types of fractal compression on a video sequence. We found that in the case of using the spiral architecture in fractal compression, the produced or decoded image or video has a better visual quality than that produced with the conventional square system and the previously proposed simplified system. We found also that all types of fractal compression are better than the JPEG standard.