Exponential spline polynomials (E-splines) represent the best smooth transition between continuous and discrete domains. As they are constructed from convolution of exponential segments, there are many degrees of freedom to optimally choose the most convenient E-spline; suitable for a specific application. In this paper, the parameters of these Esplines are optimally chosen, to sharpen the performance of an interpolated high resolution systems HR derived from a given low resolution decimated one whether noisy or noiseless. The proposed technique is based on minimizing the aliasing effects due to the high frequency bands of the HR images. Illustrative examples are given to verify image enhancement of the proposed E-spline scheme, when compared with the existing approaches.

We consider the problem of sampling non band limited signals with a finite number of degrees of freedom such as non uniform splines or piecewise polynomials. These signals are typically called signals with finite rate of innovation (FRI). We propose a novel technique for perfectly reconstructing impulses of Diracs. These Diracs are our adopted non band limited signal and have been filtered specifically through a B-spline sampling kernel, and then been uniformly sampled with a period T. This B-spline sampling kernel has an impulse response that is similar to most linear acquisition sensors/devices. The novelty of our proposed approach lies in the fact it is robust in noisy environments, unlike many recent similar techniques, i.e. Dragotti el.[1] that may provide faster implementation but are very delicate with any type of noise. Our technique also does not have any restrictions on the number of perfectly reconstructed Diracs with respect to the sampling kernel order and achieves its reconstruction in a B-spline 2-channel perfect reconstruction (PR) framework. A comparison of our proposed B-spline based perfect reconstruction system with the recent technique given in [1], in terms of speed, complexity, and kernel order complexity, is provided.

Many forensic techniques recently tried to detect the tampering and manipulation of JPEG compressed images that became a critical problem in different imaging applications. Some techniques indicated that a knowledge able attacker can make it very hard to detect image tampering, while others indicated that portions of the compressed image that has been compressed at different compression parameters can be detected, if they are recompressed after changing some of these parameters. In this project, we pursue the idea of analyzing forensically suspect-able images to detect forgery. We study the effect of adopting Nonorthogonal Discrete Cosine Transform (NDCT) that is highly utilized in efficient media implementations, in detecting if different parts of the image have been modified. This is performed by measuring block convergence of different image parts and detecting its stability after recompressions.

Single image super resolution has become an important topic in many imaging applications especially that it has a more constrained environment than regular multi image super resolution. In this paper we propose a novel single image super resolution technique that can significantly enhance a single image based on local data and statistics without a need for any prior information. The proposed algorithm is based on injecting Laplacian energy in high frequency details and estimating missing information from matched other parts of the image. Interpolation and zooming are achieved for the initial low resolution image through Exponential spline (E-spline) interpolation followed by Independent Component Analysis (ICA)separation to enhance the quality of the final high resolution image. A detailed comparison between E-spline and B-spline interpolation for the output image as well as another comparison with recent literature techniques are presented. Further enhanced results with ICA processing are also demonstrated.

In this paper we present the topic of sampling of signals that are not band limited 60 years after the well known Shannon-Nyquist sampling theory. We consider the sampling process of several signals that were not exactly considered or treated by Shannon. We can call them non band limited signals. Research in sampling of non band limited signals is divided into two main categories. Signals that are sensed using modern state of the art compressive sensing techniques, and signals with a finite number of degrees of freedom that are sensed through sampling kernels that are physically realizable. These latter types of signals are typically called signals with finite rate of innovation. We present our results with these two main categories with different images and signals. Illustrative examples of the proposed techniques are presented.

Many recent techniques for forgery detection tried to counter noise dithering, which is considered to be the most successful technique for removing footprints of JPEG editing in countering forensics. In this paper we propose a novel idea of detecting any noise dithering that is typically adopted in removing footprints in counter anti forensics of images. This technique is based on detecting phase variations for DCT coefficients, for decoded JPEG images. We try to measure the level of coherence of phase values for coefficients and detect thresholded variations that would indicate some editing or tampering of images. The proposed technique is robust against noise dithering due to the fact that local homogeneous regions inherit distinctive phase values. These phase values are inconsistent with embedded or dithered noise signals that are considered to be out of phase and can be easily detected in noisy environments. Our proposed technique is compared with literature techniques for performance in noisy applications.

In this paper we propose to develop novel techniques for signal/image decomposition, and reconstruction based on the B-spline mathematical functions. Our proposed B-spline based multiscale/resolution representation is based upon a perfect reconstruction analysis/synthesis point of view. Our proposed B-spline analysis can be utilized for different signal/imaging applications such as compression, prediction, and denoising.We also present a straightforward computationally efficient approach for B-spline basis calculations that is based upon matrix multiplication and avoids any extra generated basis. Then we propose a novel technique for enhanced B-spline based compression for different image coders by preprocessing the image prior to the decomposition stage in any image coder. This would reduce the amount of data correlation and would allow for more compression, as will be shown with our correlation metric. Extensive simulations that have been carried on the well known SPIHT image coder with and without the proposed correlation removal methodology are presented. Finally, we utilized our proposed B-spline basis for denoising and estimation applications. Illustrative results that demonstrate the efficiency of the proposed approaches are presented.

The Bspline mathematical functions have long been utilized for signal representation, zooming and interpola-tion. In this paper we propose a novel technique for preprocessing signals/images prior to the decomposition stage in dif-ferent image coders based on the Bspline decomposition for enhanced compression performance. Bspline coefficients have been traditionally calculated through inverse filtering using a causal/non-causal manner, which makes it non practical for online applications. More over Bsplines are known to be integer coefficients and representations as they are the exact mathematical translators between the discrete and continuous versions of signals. In this paper we also propose a novel implementation technique for Bspline coefficient calculation. This technique is based on a straight forward calculation approach through a Toeplitz matrix that allows parallel processing for online applications. The proposed technique is also suitable for integer coefficients as in the Bspline case. Simulation results that demonstrate the effectiveness of the proposed techniques as well as complexity analysis are presented.

Sub-band coding has long been utilized and adopted in different compression, coding and reconstruction techniques in most signal processing applications. It has wide applications in communications, bit rate codec’s, sampling,and compression for images, videos and speech. However sub-band coding systems in general suffer from a certain amount of shift variance of the output reconstructed signal, due to the frequency overlap between different sub-bands in the analysis stage. This overlap is known as non-ideal anti-aliasing. In this paper we simplify the shift variance analysis of sub-band coding systems in general, and we present different metrics that have been reported in the literature to measure the bounds of shift variance for Perfect Reconstruction (PR) sub-band systems, we simplify its mathematical analysis and illustrate with graphs the reasons for these bounds and compare them. We apply these metrics on Biorthogonal, Orthogonal and Bspline wavelets and present the worst case scenario for different input signals in terms of shift variance for all these sub-band coding systems, both numerically and graphically. We finally compare the shift variance behavior for different sub-band PR systems for different types of input signals.

Image watermarking, authentication and encryption have gained an increased importance during the last decade. This is due to the widespread use of visual media over the Internet and in several digital media applications. Several watermarking techniques have been proposed, some in spatial domain, and more recently in the transform/frequency domain and have been reported to be robust against different attacks, namely compression. It is also well known the importance and effectiveness of compression techniques to store transmit and retrieve visual information. However, the creation or development of a joint watermarking and compression framework for images has yet to be explored, where watermarking and compression could be pursued jointly on a trade-off manner. In other words, watermarking embedding/extraction can be performed on compressed domain data, while compression parameters could be used as watermarking keys. The primary focus of this paper is to explore this novel/unique idea. We propose a joint watermarking and compression (JWC) technique in the transform domain. This transform domain is based on the Natural Preserve Transform and can be utilized to achieve a balance between watermarking and compression for visual information. Watermarking performance is evaluated blindly for different compressed domain data scenarios, while compression performance is analyzed for other watermarking cases. Extensive simulation results that demonstrate the efficiency of the proposed joint watermarking and compression technique are presented.