Rank-deficient and discrete ill-posed problems: numerical aspects of linear inversion
Rank-deficient and discrete ill-posed problems: numerical aspects of linear inversion
The conjugate gradient regularization method in computed tomography problems
Applied Mathematics and Computation
Digital Image Processing
Regularization methods in dynamic MRI
Applied Mathematics and Computation
Quantitative Fourier analysis of approximation techniques. I.Interpolators and projectors
IEEE Transactions on Signal Processing
Convolution-based interpolation for fast, high-quality rotation of images
IEEE Transactions on Image Processing
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In this work we propose the use of B-spline functions for the parametric representation of high resolution images from low sampled data in the Fourier domain. Traditionally, exponential basis functions are employed in this situation, but they produce artifacts and amplify the noise on the data. We present the method in an algorithmic form and carefully consider the problem of solving the ill-conditioned linear system arising from the method by an efficient regularization method.Two applications of the proposed method to dynamic Magnetic Resonance images are considered. Dynamic Magnetic Resonance acquires a time series of images of the same slice of the body; in order to fasten the acquisition, the data are low sampled in the Fourier space. Numerical experiments have been performed both on simulated and real Magnetic Resonance data. They show that the B-splines reduce the artifacts and the noise in the representation of high resolution Magnetic Resonance images from low sampled data.