Abstract — Image interpolation techniques often are required in medical imaging for image generation (e.g., discrete back projection for inverse Radon transform) and processing such as compression or resampling. Since the ideal interpolation function spatially is unlimited, several interpolation kernels of finite size have been introduced. This paper compares 1) truncated and windowed sinc; 2) nearest neighbor; 3) linear; 4) quadratic; 5) cubic B-spline; 6) cubic; g) Lagrange; and 7) Gaussian interpolation and approximation techniques with kernel sizes from 1 2 1upto 8 2 8. The comparison is done by: 1) spatial and Fourier analyses; 2) computational complexity as well as runtime evaluations; and 3) qualitative and quantitative interpolation error determinations for particular interpolation tasks which were taken from common situations in medical image processing. For local and Fourier analyses, a standardized notation is introduced

This paper presents a chronological overview of the developments in interpolation theory, from the earliest times to the present date. It brings out the connections between the results obtained in different ages, thereby putting the techniques currently used in signal and image processing into historical perspective. A summary of the insights and recommendations that follow from relatively recent theoretical as well as experimental studies concludes the presentation. Keywords—Approximation, convolution-based interpolation, history, image processing, polynomial interpolation, signal processing, splines. “It is an extremely useful thing to have knowledge of the true origins of memorable discoveries, especially those that have been found not by accident but by dint of meditation. It is not so much that thereby history may attribute to each man his own discoveries and others should be encouraged to earn like commendation, as that the art of making discoveries should be extended by considering noteworthy examples of it. ” 1 I.

This paper describes the basis for techniques such as stochastic subdivision in the theory of random processes and estimation theory. The popular stochastic subdivision construction is then generalized to provide control of the autocorrelation and spectral properties of the synthesized random functions. The generalized construction is suitable for generating a variety of perceptually distinct high-quality random functions, including those with non-fractal spectra and directional or oscillatory characteristics. It is argued that a spectral modeling approach provides a more powerful and somewhat more intuitive perceptual characterization of random processes than does the fractal model. Synthetic textures and terrains are presented as a means of visually evaluating the generalized subdivision technique. Categories and Subject Descriptors: I.3.3 [Computer Graphics]: Picture/Image Generation; I.3.7 [Computer Graphics]: Three Dimensional Graphics and Realism -<F11.

We consider the problem of interpolating a signal using a linear combination of shifted versions of a compactly-supported basis function ( ). We first give the expression of the 's that have minimal support for a given accuracy (also known as "approximation order"). This class of functions, which we call maximal -order-minimal-support functions (MOMS) is made of linear combinations of the B-spline of same order and of its derivatives.

Nearest-neighbour, linear, and various cubic interpolation functions are frequently used in image resampling. Quadratic functions have been disregarded, largely because they have been thought to introduce phase distortions. This is shown not to be the case, and a family of quadratic functions is derived. The interpolating member of this family has visual quality close to that of the Catmull-Rom cubic, yet requires only sixty percent of the computation time.

When expanding digital signal processing of mobile communications terminals toward the antenna while making the terminal more wideband in order to be able to cope with different mobile communications standards in a software-radio-based terminal, the designer is faced with strong requirements such as bandwidth and dynamic range. Many publications claim that only reconfigurable hardware such as FPGAs can simultaneously cope with such diversity and requirements. Starting with considerations of the receiver architecture, we describe key functionalities of the digital front-end and highlight how signal characteristics of mobile communications signals and commonalities among different signal processing operations can be exploited to great advantage, eventually enabling implementations on an ASIC that, although not reconfigurable, would empower the software radio concept.

Software radio terminals must be able to process different communications standards which are generally based on different master clock rates and thus employ different bit/chip-rates. A straightforward solution to cope with this diversity of master clock rates in one terminal is to employ dedicated master clocks for each standard of operation. Being too costly in most cases, this kind of solution moreover limits the applicability of a once realized and thus fixed terminal. The smart solution to this problem is to run the terminal on a fixed clock rate, and to perform digital sample rate conversion that can be controlled by software and thus, empowers the software radio concept.

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This dissertation considers several aspects of the process

Sampling and reconstruction are usually analyzed under the framework of linear signal processing. Powerful tools like the Fourier transform and optimum linear filter design techniques, allow for a very precise analysis of the process. In particular, an optimum linear filter of any length can be derived under most situations. Many of these tools are not available for non-linear systems, and it is usually difficult to find an optimum non-linear system under any criteria. In this paper we analyze the possibility of using non-linear filtering in the interpolation of subsampled images. We show that a very simple (5x5) non-linear reconstruction filter outperforms (for the images analyzed) linear filters of up to 256x256, including optimum (separable) Wiener filters of any size. 1. INTRODUCTION In digital signal processing, it is often necessary to alter the sampling rate of a discrete signal. We usually refer to decimation (or sub-sampling) as the operation of selecting a subset of the or...