Sharif Digital Repository

Radial Basis Function, a neural network based interpolation method, is used to simulate swirling spray phenomenon. From this model, the profile of mean velocity components' distribution along the main axis of the injector at various pressure drops and spray measurements' plane are obtained and analyzed. Experimental data obtained through Phase Doppler Anemometer is used to train this model. The results are compared with experimental data as well as to those obtained through General Regression Neural Network method as another neural network based interpolation method investigated previously by the authors. © 2003 by M.R. Soltani  

Let ℒ and script N be propositional languages over Basic Propositional Calculus, and script M = ℒ ∩ script N. We prove two different but interrelated interpolation theorems. First, suppose that Π is a sequent theory over ℒ, and Σ ∪ {C ⇒ C′} is a set of sequents over script N, such that Π, Σ ⊢ C ⇒ C′. Then there is a sequent theory Φ over script N such that Π ⊢ Φ and Φ, Σ ⊢ C ⇒ C′. Second, let A be a formula over ℒ, and C1, C2 be formulas over script N, such that A ∧ C1 ⊢ C2. Then there exists a formula B over script M such that A ⊢ B and B ∧ C1 ⊢ C2  

Many high performance steganographic schemes work at a limited or sparsely distributed set of embedding rates. We have shown that some steganographic changes will be wasted as these schemes are utilized individually for messages of various lengths. To measure the wasted changes and compare different schemes in this respect, we have built a framework based on two new criteria: the Relative Change Waste (RCW) and the Expected Changes per Pixel (ECP). To decrease the wasted changes a systematic combination of schemes is introduced and proved to be equivalent to nonlinear interpolation of points in a two-dimensional space. We have proved that a special case which leads to a linear interpolation... 

The Necklace Hypecube has been recently proposed as an attractive topology for multicomputers and was shown to have many desirable properties such as well-scalability and suitability for VLSI implementation. This paper introduces a parallel algorithm for computing an N-point Lagrange interpolation on a necklace hypercube multiprocessor. This algorithm consists of 3 phases: initialization, main and final. There is no computation in the initialization phase. The main phase consists of [E/2] steps (with E being the number of edges of the network), each consisting of 4 multiplications and 4 subtractions, and an additional step including 1 division and 1 multiplication. Communication in the main... 

In this paper we extended a previously investigated modular method that is designed to compensate for interpolation distortions of one-dimensional signals, to two dimensions (2-D). Next the proposed 2-D modular technique was applied in an iterative fashion and was shown through both simulations and theoretical analyses to enhance the convergence of the iterative technique. In fact, with only a few modules we were able to achieve drastic improvements in signal reconstruction, and with a much less computational complexity. Moreover, both the simulations and the theoretical analysis confirmed the robustness of the proposed scheme against additive noise  

We introduce two Gentzen-style sequent calculus axiomatizations for conservative extensions of basic propositional logic. Our first axiomatization is an ipmrovement of [1], in the sense that it has a kind of the subformula property and is a slight modification of [6]. In this system the cut rule is eliminated. The second axiomatization is a classical conservative extension of basic propositional logic. Using these axiomatizations, we prove interpolation theorems for basic propositional logic. © 2001 Kluwer Academic Publishers  

This paper reports the results of SIMD implementation of a number of interpolation algorithms on common personal computers. These methods fit a curve on some given input points for which a mathematical function form is not known. We have implemented four widely used methods using vector processing capabilities embedded in Pentium processors. By using SSE (streaming SIMD extension) we could perform all operations on four packed single-precision (32-bit) floating point values simultaneously. Therefore, the running time decreases three times or even more depending on the number of points and the interpolation method. We have implemented four interpolation methods using SSE technology then... 

The maximally flat (MF) fractional delay (FD) filter which is in fact a Lagrange interpolator for uniformly sampled signals, has previously been shown to be equal to the scaled binomially windowed shifted version of the sinc function; the ideal interpolation kernel for band-limited signals. In this paper, another proof for this equivalence is presented. Unlike its counterparts available in the literature, the proof given here is neither strictly algebraic, nor deploys the explicit coefficient formulas of the MFFD filter. It follows a frequency domain approach based on the definition of this filter instead, and aims to provide more insight into the corresponding equivalence. © 2009 Elsevier... 

This article introduces a new adaptive method for image interpolation. In order to obtain a high resolution (HR) image from its low resolution (LR) counterpart (original image), an interpolator function (array) is used, and the main focus of this manuscript is to formulate and define this function. By applying this interpolator function to each row and column of a LR image, it is possible to construct its HR counterpart. One of the main challenges of image interpolation algorithms is to maintain the edge structures while developing an HR image from the LR replica. The proposed approach overcomes this challenge and exhibits remarkable results at the image edges. The peak signal to noise ratio... 

In this paper, we investigate the problem of designing compact-support interpolation kernels for a given class of signals. By using calculus of variations, we simplify the optimization problem from an nonlinear infinite dimensional problem to a linear finite dimensional case, and then find the optimum compact-support function that best approximates a given filter in the least square sense (ℓ 2 norm). The benefit of compact-support interpolants is the low computational complexity in the interpolation process while the optimum compact-support interpolant guarantees the highest achievable signal-to-noise ratio (SNR). Our simulation results confirm the superior performance of the proposed kernel... 

In this paper we address the problem of image interpolation using Gaussian Mixture Models (GMM) as a prior. Previous methods of image restoration with GMM have not considered spatial (geometric) distance between patches in clustering, failing to fully exploit the coherency of nearby patches. The GMM framework in our method for image interpolation is based on the assumption that the accumulation of similar patches in a neighborhood are derived from a multivariate Gaussian probability distribution with a specific covariance and mean. An Expectation Maximization-like (EM-like) algorithm is used in order to determine patches in a cluster and restore them. The results show that our image... 

This paper presents three schemes of 2D meshless finite volume (MFV) method, referred to as MFV with overlapping control volumes (MFV1), MFV with irregular non-overlapping control volumes (MFV2) and MFV with regular non-overlapping control volumes (MFV3). The methods utilize the local symmetric weak form of system equation and the interpolation functions constructed using the weighted multi-triangles method (WMTM) which is recently developed by the present authors. The proposed formulation involves only integrals over the boundaries of control volumes. The performance of the proposed schemes is studied in three benchmark problems. A comparative study between the predictions of the above MFV... 

We study Basic algebra, the algebraic structure associated with basic propositional calculus, and some of its natural extensions. Among other things, we prove the amalgamation property for the class of Basic algebras, faithful Basic algebras and linear faithful Basic algebras. We also show that a faithful theory has the interpolation property if and only if its correspondence class of algebras has the amalgamation property. © 2006 Springer-Verlag  

Blotches are the common artifacts in degraded motion picture sequences. They are usually caused by placing dust and dirt on film surfaces as well as abrasion of film materials. Blotches are seen as dark and bright flashes spreading through the frames, randomly. The spike detection index (SDIa) method is the simplest approach used to detect these artifacts. However, when the motion vectors are not precise enough in some points they might be declared as blotches too. This situation can also occur in areas containing a high level of noise. To overcome these difficulties, two post-processing methods are proposed in this paper. In the first method, the edge points are first omitted from the set... 

This paper introduces a parallel algorithm for computing an N = n2n point Lagrange interpolation on an n-dimensional cube-connected cycles (CCCn). The algorithm consists of three phases: initialisation, main and final. While there is no computation in the initialisation phase, the main phase is composed of n2n-1 steps, each consisting of four multiplications, four subtractions and one communication operation, and an additional step including one division and one multiplication. The final phase is carried out in two sub-phases. There are [n/2] steps in the first sub-phase, each including two additions and one communication, followed by the second sub-phase which comprises n steps each... 

Although the fractional delay filtering literature is full of design methods and implementation techniques for fractional sample interpolators, a fundamental need for the proposition of low-order efficient designs still strongly exists. Proposed is such a system for half-sample interpolation. In contrast to the typical systems studied in the literature for fractional delay filtering, the system proposed continuously adapts its interpolation kernel to the statistical variations of the input signal, and this is in fact the reason for it being needless of having a high order. Satisfactory performance of the proposed structure has been demonstrated via simulation  

Mesh-based motion estimation is an important tool for video coding especially with low bit rate. In this paper, a new method for interpolating pixel motion from adjacent mesh nodes with the ability of omitting independent nodes is proposed. By exploiting fuzzy rules to determine the association of pixel and neighboring nodes, the proposed interpolation can detach pixels from some nodes. Consequently, it can deal with those critical patches on objects boundary which their nodes do not belong to one object. Updating the membership functions of each rule with specified strategy makes the interpolation adaptive with non-stationary conditions of image sequences and decreases sensitivity to... 

Multivariate interpolation and approximation is a powerful tool for intuition of real world. In this paper we study Lebesgue function and Lebesgue constant for multivariate interpolation by conditionally positive definite RBFs. Also we give a conjecture about similar Bernstein and Erdös problem to multivariate case. © 2006 Elsevier Inc. All rights reserved  

The maximally flat (MF) fractional delay (FD) filter which is in fact a Lagrange interpolator for uniformly sampled signals, has previously been shown to be equal to the scaled binomially windowed shifted version of the sinc function; the ideal interpolation kernel for band-limited signals. In this paper, another proof for this equivalence is presented. Unlike its counterparts available in the literature, the proof given here is neither strictly algebraic, nor deploys the explicit coefficient formulas of the MFFD filter. It follows a frequency domain approach based on the definition of this filter instead, and aims to provide more insight into the corresponding equivalence. © 2009 Elsevier... 

Temporal interpolation has been recently proposed as a solution for increasing temporal resolution or even for predicting missing or corrupted frames within a video sequence . In this paper new technique on temporal interpolation are presented, by mainly exploiting properties of the very popular and highly efficient transforms such as Discrete Cosine Transform and Discrete Wavelet Transform . Novelty of the approach is that resolution enhancement is done by adding the new coefficients in transform domain . In addition we further give a method for computing PSNR of the frames . Finally simulation on a number of video sequences is presented in order to compare the performance of this two...