Publications related to A fast iterative thresholding algorithm for wavelet-regularized deconvolution - art. no. 67010D

Wavelet analysis of the Besov regularity of Levy white noise

Julien René Pierre Fageot, Shayan Aziznejad

We characterize the local smoothness and the asymptotic growth rate of the Levy white noise. We do so by characterizing the weighted Besov spaces in which it is located. We extend known results in two ways. First, we obtain new bounds for the local smoothn ...

2020

Wavelet Steerability and the Higher-Order Riesz Transform

Michaël Unser, Dimitri Nestor Alice Van De Ville

Our main goal in this paper is to set the foundations of a general continuous-domain framework for designing steerable, reversible signal transformations (a.k.a. frames) in multiple dimensions (d ≥ 2). To that end, we introduce a self-reversible, Nth-order ...

Institute of Electrical and Electronics Engineers2010

On the Shiftability of Dual-Tree Complex Wavelet Transforms

Michaël Unser, Kunal Narayan Chaudhury

The dual-tree complex wavelet transform (DT-ℂWT) is known to exhibit better shift-invariance than the conventional discrete wavelet transform. We propose an amplitude-phase representation of the DT-ℂWT which, among other things, offers a direct explanation ...

IEEE2010

Wavelet Primal Sketch Representation Using Marr Wavelet Pyramid and Its Reconstruction

Michaël Unser, Dimitri Nestor Alice Van De Ville

Based on the class of complex gradient-Laplace operators, we show the design of a non-separable two-dimensional wavelet basis from a single and analytically defined generator wavelet function. The wavelet decomposition is implemented by an efficient FFT-ba ...

SPIE2009

Construction of Hilbert Transform Pairs of Wavelet Bases and Gabor-Like Transforms

Michaël Unser, Kunal Narayan Chaudhury

We propose a novel method for constructing Hilbert transform (HT) pairs of wavelet bases based on a fundamental approximation-theoretic characterization of scaling functions-the B-spline factorization theorem. In particular, starting from well-localized sc ...

IEEE2009

Gabor Wavelet Analysis and the Fractional Hilbert Transform

Michaël Unser, Kunal Narayan Chaudhury

We propose an amplitude-phase representation of the dual-tree complex wavelet transform (DT-ℂWT) which provides an intuitive interpretation of the associated complex wavelet coefficients. The representation, in particular, is based on the shifting action o ...

SPIE2009

Complex Wavelet Bases, Steerability, and the Marr-Like Pyramid

Michaël Unser, Dimitri Nestor Alice Van De Ville

Our aim in this paper is to tighten the link between wavelets, some classical image-processing operators, and David Marr's theory of early vision. The cornerstone of our approach is a new complex wavelet basis that behaves like a smoothed version of the Gr ...

Institute of Electrical and Electronics Engineers2008

The Marr Wavelet Pyramid

Michaël Unser, Dimitri Nestor Alice Van De Ville

We introduce a new semi-orthogonal complex wavelet basis of

L _{ 2 }

(\mathbb{R} ^{ 2 }

). The basis functions are associated to the complex gradient-Laplace operator, which plays a central role in image processing. We define analytically a single- ...

IEEE2008

The Monogenic Riesz-Laplace Wavelet Transform

Michaël Unser, Dimitri Nestor Alice Van De Ville, Katarina Balac

We introduce a family of real and complex wavelet bases of

L _{ 2 }

(\mathbb{R} ^{ 2 }

) that are directly linked to the Laplace and Riesz operators. The crucial point is that the family is closed with respect to the Riesz transform which maps a re ...

EURASIP2008

A Fast Iterative Thresholding Algorithm for Wavelet-Regularized Deconvolution

Michaël Unser, Cédric René Jean Vonesch

We present an iterative deconvolution algorithm that minimizes a functional with a non-quadratic wavelet-domain regularization term. Our approach is to introduce subband-dependent parameters into the bound optimization framework of Daubechies et al.; it is ...

SPIE2007

A fast iterative thresholding algorithm for wavelet-regularized deconvolution - art. no. 67010D

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Wavelet analysis of the Besov regularity of Levy white noise

Wavelet Steerability and the Higher-Order Riesz Transform

On the Shiftability of Dual-Tree Complex Wavelet Transforms

Wavelet Primal Sketch Representation Using Marr Wavelet Pyramid and Its Reconstruction

Construction of Hilbert Transform Pairs of Wavelet Bases and Gabor-Like Transforms

Gabor Wavelet Analysis and the Fractional Hilbert Transform

Complex Wavelet Bases, Steerability, and the Marr-Like Pyramid

The Marr Wavelet Pyramid

The Monogenic Riesz-Laplace Wavelet Transform

A Fast Iterative Thresholding Algorithm for Wavelet-Regularized Deconvolution

Wavelet analysis of the Besov regularity of Levy white noise

Wavelet Steerability and the Higher-Order Riesz Transform

Complex Wavelet Bases, Steerability, and the Marr-Like Pyramid

Wavelet Primal Sketch Representation Using Marr Wavelet Pyramid and Its Reconstruction

On the Shiftability of Dual-Tree Complex Wavelet Transforms

Construction of Hilbert Transform Pairs of Wavelet Bases and Gabor-Like Transforms

Gabor Wavelet Analysis and the Fractional Hilbert Transform

The Marr Wavelet Pyramid

The Monogenic Riesz-Laplace Wavelet Transform

A Fast Iterative Thresholding Algorithm for Wavelet-Regularized Deconvolution