Inverse polynomial reconstruction method in DCT domain

Dadkhahi, Hamid; Gotchev, Atanas; Егиазарян, Карен

doi:10.1186/1687-6180-2012-133

Cited by 4 publications

(3 citation statements)

References 35 publications

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“…Spectral approximations have been widely implemented in the approximation of signals [20,21]. The kernel functions very commonly used in spectral partial sum approximations are Fourier, Cosine, Legendre, Chebyshev, and Gegenbauer, and so forth.…”

Section: Coshad-based Iprm Is Spectrally Convergentmentioning

confidence: 99%

Discrete Fractional COSHAD Transform and Its Application

Zhu

Gui

Zhu

et al. 2014

Mathematical Problems in Engineering

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In recent years, there has been a renewed interest in finding methods to construct orthogonal transforms. This interest is driven by the large number of applications of the orthogonal transforms in image analysis and compression, especially for colour images. Inspired by this motivation, this paper first introduces a new orthogonal transform known as a discrete fractional COSHAD (FrCOSHAD) using the Kronecker product of eigenvectors and the eigenvalues of the COSHAD kernel functions. Next, this study discusses the properties of the FrCOSHAD kernel function, such as angle additivity. Using the algebra of quaternions, the study presents quaternion COSHAD/FrCOSHAD transforms to represent colour images in a holistic manner. This paper also develops an inverse polynomial reconstruction method (IPRM) in the discrete COSHAD/FrCOSHAD domains. This method can effectively recover a piecewise smooth signal from the finite set of its COSHAD/FrCOSHAD coefficients, with high accuracy. The convergence theorem has proved that the partial sum of COSHAD provides a spectrally accurate approximation to the underlying piecewise smooth signal. The experimental results verify the numerical stability and accuracy of the proposed methods.

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Section: Coshad-based Iprm Is Spectrally Convergentmentioning

confidence: 99%

Discrete Fractional COSHAD Transform and Its Application

Zhu

Gui

Zhu

et al. 2014

Mathematical Problems in Engineering

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“…We close this special issue by two papers [22,23] devoted to the topic of rapidly emerging sparse reconstruction and compressed sensing approaches. Puy et al present in [22] a 'spread spectrum' compressed sensing strategy.…”

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confidence: 99%

“…Finally, Dadkhahi et al [23] offer a different approach to sparse representations: a reprojection of a signal represented in one basis onto another basis. In particular, the authors concentrate on constructing the sparse representation of piecewise smooth signals using the discrete cosine transform (DCT) by deriving the inverse polynomial reconstruction method for the DCT expansion.…”

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confidence: 99%

Advanced statistical tools for enhanced quality digital imaging with realistic capture models

Pižurica

Portilla

Hirakawa

et al. 2013

EURASIP J. Adv. Signal Process.

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EditorialGetting closer to reality in modeling image capture devices is crucial for the improvement of image quality beyond the limits of image restoration algorithms as we know them today. This calls for more accurate statistical modeling of distortions and noise coming from real capture devices (Poisson noise, internal non-linearities, space variant point spread functions due to nonideal optics, chromatic aberrations, etc.). While these effects are often not considered in the restoration algorithms, their impact on the resulting image quality is huge in practice. For example, different nonlinearities (both intrinsic to the imaging device and induced ones, e.g., to make the noise signal independent) can invalidate typically assumed noise models and can also devastate deblurring. Joint modeling of digital and nondigital components (like optics and sensors) or various sources of image distortions (such as color filter array, blur, and noise) will likely yield improvements over the traditional approach to treat them separately. Rapid progress in digital camera technology makes a huge impact on computer vision, surveillance and security systems, production of portable electronic devices, such as smart phones. Physical limits of the sensors are likely to impose trade-offs on picture quality (e.g., in terms of achievable resolution versus noise considerations) that can be dealt with only by smart and device-aware signal processing. Moreover, new challenges arise from new imaging technologies, like in three-dimensional (3D) digital cameras [1,2], and new acquisition modalities, such as compressive sensing [3][4][5][6][7].One of the central topics to this special issue is realistic modeling of noise in digital cameras. With ongoing miniaturization, sensor elements of the camera are becoming increasingly sensitive to noise. In state-of-the-art image sensors, the pixel size is approaching 1 μm. By shrinking the pixel size towards the wavelengths of light that *Correspondence: sanja@telin.ugent.be 1 Department of Telecommunications and Information Processing, Ghent University, Gent 9000, Belgium Full list of author information is available at the end of the article the camera captures, the amount of light received will be further decreased by technical barriers (diffraction effects) [8]. Hence, increasing further the sensor resolution by itself will not necessarily lead to actual gains in image quality. Also, recent improvements in sensor sensitivity allow cameras to operate in very low lighting conditions, but this boosts noise in the acquired images. The negative effects of noise can be largely suppressed by post-processing algorithms, but these require precise knowledge of the noise characteristics to achieve optimal performance. Due to the mismatch between the actual noise characteristics and typically assumed, simplified noise models, the noise level is typically over-or underestimated, affecting adversely the performance of noise reduction.Three papers in this special issue [9][10][11] address the problem of camera ...

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Representation of Functions in Basis Sets

Shizgal

2015

Scientific Computation

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Inverse polynomial reconstruction method in DCT domain

Cited by 4 publications

References 35 publications

Discrete Fractional COSHAD Transform and Its Application

Discrete Fractional COSHAD Transform and Its Application

Advanced statistical tools for enhanced quality digital imaging with realistic capture models

Representation of Functions in Basis Sets

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