Publications by Ildar Khalidov

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In this paper, an approach is introduced based on differential operators to construct wavelet-like basis functions. Given a differential operator L with rational transfer function, elementary building blocks are obtained that are shifted replicates of the ...

The connection between derivative operators and wavelets is well known. Here we generalize the concept by constructing multiresolution approximations and wavelet basis functions that act like Fourier multiplier operators. This construction follows from a s ...

We build a multiresolution analysis based on shift-invariant exponential B-spline spaces. We construct the basis functions for these spaces and for their orthogonal complements. This yields a new family of wavelet-like basis functions of

L _{ 2 }

, wit ...

Tomographic reconstruction from positron emission tomography (PET) data is an ill-posed problem that requires regularization. An attractive approach is to impose an

\ell_{ 1 }

-regularization constraint, which favors sparse solutions in the wavelet dom ...

We introduce a new class of wavelets that behave like a given differential operator L. Our construction is inspired by the derivative-like behavior of classical wavelets. Within our framework, the wavelet coefficients of a signal y are the samples of a smo ...

Magnetic resonance spectroscopy imaging (MRSI) is a promising and developing tool in medical imaging. Because of various difficulties imposed by the imperfections of the scanner and the reconstruction algorithms, its applicability in clinical practice is r ...

Magnetic resonance spectroscopy imaging (MRSI) is an attractive tool for medical imaging. However, its practical use is often limited by the intrinsic low spatial resolution and long acquisition time. Spectral localization by imaging (SLIM) has been propos ...

We build wavelet-like functions based on a parametrized family of pseudo-differential operators

L _{ v }

that satisfy some admissibility and scalability conditions. The shifts of the generalized B-splines, which are localized versions of the Green func ...

We propose a new framework to extract the activity-related component in the BOLD functional magnetic resonance imaging (fMRI) signal. As opposed to traditional fMRI signal analysis techniques, we do not impose any prior knowledge of the event timing. Inste ...

Ildar Khalidov

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From Differential Equations to the Construction of New Wavelet-Like Bases

Operator-Like Wavelet Bases of $ L _{ 2 } $ $ (\mathbb{R} ^{ d } $ )

Exponential-Spline Wavelet Bases

Dynamic PET Reconstruction Using Wavelet Regularization with Adapted Basis Functions

Operator-like wavelets with application to functional magnetic resonance imaging

Improved MRSI with Field Inhomogeneity Compensation

BSLIM: Spectral Localization by Imaging with Explicit $ B _{ 0 } $ Field Inhomogeneity Compensation

Generalized L-Spline Wavelet Bases

Reconstruction of Dynamic PET Data Using Spatio-Temporal Wavelet $ ℓ _{ 1 } $ Regularization

Activelets: Wavelets for sparse representation of hemodynamic responses