The FFT is used widely in signal processing for efficient computation of the Fourier transform (FT) of finitelength signals over a set of uniformly-spaced frequency locations. However, in many applications, one requires nonuniform sampling in the frequency domain, i.e.,a nonuniform FT . Several papers have described fast approximations for the nonuniform FT based on interpolating an oversampled FFT. This paper presents an interpolation method for the nonuniform FT that is optimal in the min-max sense of minimizing the worst-case approximation error over all signals of unit norm. The proposed method easily generalizes to multidimensional signals. Numerical results show that the min-max approach provides substantially lower approximation errors than conventional interpolation methods. The min-max criterion is also useful for optimizing the parameters of interpolation kernels such as the Kaiser-Bessel function.

Scalability and others functionalities such as the Region of Interest encoding become essential properties of an efficient image coding scheme. Within the framework of lossless compression techniques, S+P and CALIC represent the state-of-the-art. The proposed Interleaved S+P algorithm outperforms these method while providing the desired properties. Based on the LAR (Locally Adaptive Resolution) method, an original pyramidal decomposition combined with a DPCM scheme is elaborated. This solution uses the S-transform in such a manner that a refined prediction context is available for each estimation steps. The image coding is done in two main steps, so that the first one supplies a LAR lowresolution image of good visual quality, and the second one allows a lossless reconstruction. The method exploits an implicit context modelling, intrinsic property of our content-based quad-tree like representation. 1.

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Color images in single chip digital cameras are obtained by interpolating mosaiced color samples. These samples are encoded in a single chip CCD by sampling the light after it passes through a color filter array (CFA) that contains different color filters (i.e. red, green, and blue) placed in some pattern. The resulting sparsely sampled images of the three-color planes are interpolated to obtain the complete color image. Interpolation usually introduces color artifacts due to the phase-shifted, aliased signals introduced by the sparse sampling of the CFAs. This paper introduces a non-linear interpolation scheme based on edge information that produces high quality visual results. The new method is especially good at reconstructing the image around edges, a place where the visual human system is most sensitive.

An optimal recovery based neural-network Super Resolution algorithm is developed. The proposed method is computationally less expensive and outputs images with high subjective quality, compared with previous neuralnetwork or optimal recovery algorithms. It is evaluated on classical SR test images with both generic and specialized training sets, and compared with other state-of-the-art methods. Results show that our algorithm is among the state-of-the-art, both in quality and efficiency. 1.

computer graphics and digital cameras is prevalent. High resolution display and printer are available. Therefore high resolution images are needed in order to produce high quality display images and high quality prints. However, since high resolution images are not usually provided, there is a need to magnify the original images. One common difficulty in the previous magnification techniques is that of preserving details, i.e. edges and at the same time smoothing the data for not introducing the spurious artefacts. A definitive solution to this is still an open issue. In this paper an image magnification using adaptive interpolation by pixel level data-dependent geometrical shapes is proposed that tries to take into account information about the edges (sharp luminance variations) and smoothness of the image. It calculate threshold, classify interpolation region in the form of geometrical shapes and then assign suitable values inside interpolation region to the undefined pixels while preserving the sharp luminance variations and smoothness at the same time. The results of proposed technique has been compared qualitatively and quantitatively with five other techniques. In which the qualitative results show that the proposed method beats completely the Nearest Neighbouring (NN), bilinear(BL) and bicubic(BC) interpolation. The quantitative results are competitive and consistent with NN, BL, BC and others. Keywords—Adaptive, digital image processing, image magnification, interpolation, geometrical shapes, qualitative & quantitative analysis. I.

The rapid growth in computer graphics and digital cameras has resulted in computer users being able to easily produce digital images. As a result, the need to display and print digital images has increased. Nowadays, highresolution display and printing devices are available to users. Therefore, high-resolution images are needed in order to produce high quality displayed images and high quality prints. However, since high-resolution images are not usually provided, there is a need to magnify the original images. Previous methods on magnifying images have the disadvantage that either the sharpness of the edges cannot be preserved or that some distinct artifacts are produced in the magnified image. In this paper, we present a novel method for doubling the size of images in which the sharpness of the edges is preserved without introducing distinct artifacts in the magnified images. The proposed method consists of two steps, first generation of an initial magnified image and then progressively refining this image to produce a high quality magnified image. The experimental results show that with the proposed method it is possible to produce magnified images of comparable, and in some cases superior, visual quality to those produced using previous methods. 1.

Within the framework of telemedicine, the amount of images leads first to use efficient lossless compression methods for the aim of storing information. Furthermore, multiresolution scheme including Region of Interest (ROI) processing is an important feature for a remote access to medical images. What is more, the securization of sensitive data (e.g. metadata from DICOM images) constitutes one more expected functionality: indeed the lost of IP packets could have tragic effects on a given diagnosis. For this purpose, we present in this paper an original scalable image compression technique (LAR method) used in association with a channel coding method based on the Mojette Transform, so that a hierarchical priority encoding system is elaborated. This system provides a solution for secured transmission of medical images through low-bandwidth networks such as the Internet.

The joint source-channel coding system proposed in this paper has two aims: lossless compression with a progressive mode and the integrity of medical data, which takes into account the priorities of the image and the properties of a network with no guaranteed quality of service. In this context, the use of scalable coding, Locally Adapted Resolution (LAR) and a discrete and exact Radon transform, known as the Mojette transform, meets this twofold requirement. In this paper, details of this joint coding implementation are provided as well as a performance evaluation with respect to the reference CALIC coding and to unequal error protection using Reed-Solomon codes. Key words: medical image compression; LAR method; Mojette transform; scalability; priority encoding system;

A still image codec should not only to be good from compression point of view, it might also provide services. The LAR interleaved S+P codec allows loss-less to lossy coding, presenting both resolution and distortion scalability. The proposed method brings image encryption at no cost in the LAR framework. It exploits the embedded quadtree decomposition of the LAR to provide multilevel protection to the whole bit-stream. Theoretical aspects are considered and experimental results show the effectiveness of the process. LAR CODER authorization system multilevel quadtree bitstream LAR DECODER