Image enhancement using E-spline functions (original) (raw)
Related papers
2013
B-splines caught interest of many engineering applications due to their merits of being flexible and provide a large degree of differentiability and cost/quality trade off relationship. However they have less impact with continuous time applications as they are constructed from piecewise polynomials. On the other hand, Exponential spline polynomials (E-splines) represent the best smooth transition between continuous and discrete domains as they are made of exponential segments. In this paper we present a technique for utilizing E-splines in image de-noising applications. This technique is based upon sub-band decomposition of the image through an E-spline based perfect reconstruction (PR) system. Different thresholdings are applied on the decomposition layers for de-noising purposes. Due to the selective nature of E-spline based decomposition, the performance of our E-spline based de-noising technique outperforms all other literature techniques.
B-spline wavelets for signal denoising and image compression
Signal, Image and Video Processing, 2009
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 wellknown 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.
Spline Interpolation and Wavelet Construction
Applied and Computational Harmonic Analysis, 1998
The method of Dubuc and Deslauriers on symmetric interpolatory subdivision is extended to study the relationship between interpolation processes and wavelet construction. Refinable and interpolatory functions are constructed in stages from B-splines. Their method constructs the filter sequence (its Laurent polynomial) of the interpolatory function as a product of Laurent polynomials. This provides a natural way of splitting the filter for the construction of orthonormal and biorthogonal scaling functions leading to orthonormal and biorthogonal wavelets. Their method also leads to a class of filters which includes the minimal length Daubechies compactly supported orthonormal wavelet coefficients. Examples of ''good'' filters are given together with results of numerical experiments conducted to test the performance of these filters in data compression.
A Bivariate Spline Approach for Image Enhancement
2010
A new approach for image enhancement is developed in this paper. It is based on bivariate spline functions. By choosing a local region from an image to be enhanced, one can use bivariate splines with minimal surface area to enhance the image by reducing noises, smoothing the contrast, e.g. smoothing wrinkles and removing stains or damages from images. To establish this approach, we first discuss its mathematical aspects: the existence, uniqueness and stability of the splines of minimal surface area and propose an iterative algorithm to compute the fitting splines of minimal surface area. The convergence of the iterative solutions will be established. In addition, the fitting splines of minimal surface area are convergent as the size of triangulation goes to zero in theory. Finally, several numerical examples are shown to demonstrate the effectiveness of this new approach.
Splines: A New Contribution to Wavelet Analysis
We present a new approach to the construction of biorthogonal wavelet transforms using polynomial splines. The construction is performed in a "lifting" manner and we use interpolatory, as well as local quasi-interpolatory and smoothing splines as predicting aggregates in this scheme. The transforms contain some scalar control parameters which enable their flexible tuning in either time or frequency domains. The transforms are implemented in a fast way. They demonstrated efficiency in application to image compression.
A QUICK GLANCE OF SPLINE WAVELETS AND ITS APPLICATIONS
Polynomial spline wavelets have played a momentous role in the enlargement of wavelet theory. Due to their attractive properties compact support, good smoothness property, interpolation property, they are now provide powerful tools for many scientific and practical problems. As splines have specific formulae in both time and frequency domain, it greatly facilitates their manipulation. This paper is a summary of spline wavelet which started with splines and ends with the applications of spline wavelets. The paper is divided into four sections. The first section contains a brief introduction of splines and the second section is devoted to the discussion of spline wavelet construction via multiresolution analysis (MRA) with emphasis on B-spline wavelet. The underlying scaling functions are B-splines, which are shortest and most regular scaling function. In the third section, some remarkable properties of spline wavelets are discussed. The orthogonality and finite support properties make the spline wavelets useful for numerical applications and also have the best approximation properties among all the known wavelets. And the last section enclose a brief discussion of application of spline wavelets.
Wavelet Transforms Generated by Splines
International Journal of Wavelets, Multiresolution and Information Processing, 2007
In this paper, we design a new family of biorthogonal wavelet transforms that are based on polynomial and discrete splines. The wavelet transforms are constructed via lifting steps, where the prediction and update filters are derived from various types of interpolatory and quasi-interpolatory splines. The transforms use finite and infinite impulse response (IIR) filters and are implemented in a fast lifting mode. We analyze properties of the generated scaling functions and wavelets. In the case when the prediction filter is derived from a polynomial interpolatory spline of even order, the synthesis scaling function and wavelet are splines of the same order. We formulate conditions for the IIR filter to generate an exponentially decaying scaling function.
A new Image Interpolation Technique using Exponential B-Spline
In this paper, we propose a new interpolation technique using exponential B-spline, which is super-set of the Bspline. An interpolation kernel of exponential B-spline was proposed using IIR based technique by Unser. As another approach, this paper presents an exponential B-spline interpolation kernel using simple mathematics based on Fourier approximation. A high signal to noise ratio can be achieved because exponential B-spline parameters can be set depending on the signal characteristics. The analysis of these interpolated kernels shows they have better performance in high and low frequency components as compared to other conventional nearest neighbor, linear, spline based methods.
Applied and Computational Harmonic Analysis, 2008
Spline wavelets on a hybrid of uniform and geometric meshes that admits a natural dyadic multiresolution structure are constructed. The construction is extended to other scaling functions. The hybrid splines and wavelets provide good approximation of functions near singularities and efficient representation of images with high resolution around regions of interest.