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In this paper, we first propose a new family of geometrical image transforms that decompose images both radially and angularly. Our construction comprises two stages of filter banks that are non-redundant and perfect reconstruction and therefore lead to an overall non-redundant and perfect reconstruction transform. Using the wavelet transform as the first(More)
We propose a new family of nonredundant geometrical image transforms that are based on wavelets and directional filter banks. We convert the wavelet basis functions in the finest scales to a flexible and rich set of directional basis elements by employing directional filter banks, where we form a nonredundant transform family, which exhibits both(More)
We propose a new family of perfect reconstruction, non-redundant, and multiresolution geometrical image transforms using the wavelet transform in conjunction with modified versions of directional filter banks (DFB). In the proposed versions of DFB, we use either horizontal or vertical directional decomposition. Taking advantage of the wavelet transform that(More)
Most subsampled filter banks lack the feature of translation invariance, which is an important characteristic in denoising applications. In this paper, we study and develop new methods to convert a general multichannel, multidimensional filter bank to a corresponding translation-invariant (TI) framework. In particular, we propose a generalized algorithme(More)
We introduce a novel algorithm to address the challenges in magnetic resonance (MR) spectroscopic imaging. In contrast to classical sequential data processing schemes, the proposed method combines the reconstruction and postprocessing steps into a unified algorithm. This integrated approach enables us to inject a range of prior information into the data(More)
The contourlet transform, one of the recent geometrical image transforms, lacks the feature of translation invariance due to subsampling in its filter bank (FB) structure. In this paper we develop a translation-invariant (TI) scheme of a general multi-channel multidimensional FB and apply our findings to the contourlet transform to obtain a TI contourlet(More)
PURPOSE To minimize line shape distortions and spectral leakage artifacts in MR spectroscopic imaging (MRSI). METHODS A spatially and spectrally regularized non-Cartesian MRSI algorithm that uses the line shape distortion priors, estimated from water reference data, to deconvolve the spectra is introduced. Sparse spectral regularization is used to(More)
In a previous work, we proposed a new family of nonredundant geometrical image transforms using hybrid wavelets and directional filter banks (HWD). In this paper we further develop and examine the proposed family and provide an efficient realization utilizing regular filters. Furthermore, we extend and employ the new proposed HWD transforms in two key image(More)