Publications by Pouya Dehghani Tafti

A Unified Formulation of Gaussian Versus Sparse Stochastic Processes-Part II: Discrete-Domain Theory

Michaël Unser, Pouya Dehghani Tafti, Hagay Kirshner, Arash Amini

This paper is devoted to the characterization of an extended family of continuous-time autoregressive moving average (CARMA) processes that are solutions of stochastic differential equations driven by white Levy innovations. These are completely specified ...

Ieee-Inst Electrical Electronics Engineers Inc2014

A Unified Formulation of Gaussian Versus Sparse Stochastic Processes-Part I: Continuous-Domain Theory

Michaël Unser, Pouya Dehghani Tafti

We introduce a general distributional framework that results in a unifying description and characterization of a rich variety of continuous-time stochastic processes. The cornerstone of our approach is an innovation model that is driven by some generalized ...

Ieee-Inst Electrical Electronics Engineers Inc2014

Variational Decomposition of Vector Fields in the Presence of Noise

Michaël Unser, Pouya Dehghani Tafti, Emrah Bostan

We present a variational framework, and an algorithm based on the alternating method of multipliers (ADMM), for the problem of decomposing a vector field into its curl- and divergence-free components (Helmholtz decomposition) in the presence of noise. We p ...

IEEE2013

Spatio-Temporal Regularization Of Flow-Fields

Nikolaos Stergiopoulos, Michaël Unser, Pouya Dehghani Tafti, Emrah Bostan, Orestis Vardoulis, Davide Piccini

We introduce a novel variational framework for the regularized reconstruction of time-resolved volumetric flow fields. Our objective functional takes the physical characteristics of the underlying flow into account in both the spatial and the temporal doma ...

IEEE2013

A Dual Algorithm for $ L _{ 1 } $ -Regularized Reconstruction of Vector Fields

Michaël Unser, Pouya Dehghani Tafti, Emrah Bostan

Recent advances in vector-field imaging have brought to the forefront the need for efficient denoising and reconstruction algorithms that take the physical properties of vector fields into account and can be applied to large volumes of data. With these req ...

IEEE2012

On Regularized Reconstruction of Vector Fields

Michaël Unser, Pouya Dehghani Tafti

In this paper, we give a general characterization of regularization functionals for vector field reconstruction, based on the requirement that the said functionals satisfy certain geometric invariance properties with respect to transformations of the coord ...

IEEE2011

Stochastic Models for Sparse and Piecewise-Smooth Signals

Michaël Unser, Pouya Dehghani Tafti

We introduce an extended family of continuous-domain stochastic models for sparse, piecewise-smooth signals. These are specified as solutions of stochastic differential equations, or, equivalently, in terms of a suitable innovation model; the latter is ana ...

IEEE2011

Variational Enhancement And Denoising Of Flow Field Images

Michaël Unser, Pouya Dehghani Tafti, Ricard Delgado Gonzalo

In this work we propose a variational reconstruction algorithm for enhancement and denoising of flow fields that is reminiscent of total-variation (TV) regularization used in image processing, but which also takes into account physical properties of flow s ...

Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa2011

Self-Similar Vector Fields

Pouya Dehghani Tafti

We propose statistically self-similar and rotation-invariant models for vector fields, study some of the more significant properties of these models, and suggest algorithms and methods for reconstructing vector fields from numerical observations, using the ...

EPFL2011

Fractional Brownian Models For Vector Field Data

Michaël Unser, Pouya Dehghani Tafti

In this note we introduce a vector generalization of fractional Brownian motion. Our definition takes into account directional properties of vector fields-such as divergence, rotational behaviour, and interactions with coordinate transformations-that have ...

Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa2010

Fractal Modelling And Analysis Of Flow-Field Images

Michaël Unser, Pouya Dehghani Tafti, Ricard Delgado Gonzalo

We introduce stochastic models for flow fields with parameters that dictate the scale-dependent (self-similar) character of the field and control the balance between its rotational vs compressive behaviour. The development of our models is motivated by the ...

Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa2010

Fractional Brownian Vector Fields

Michaël Unser, Pouya Dehghani Tafti

This work puts forward an extended definition of vector fractional Brownian motion (fBm) using a distribution theoretic formulation in the spirit of Gel′fand and Vilenkin's stochastic analysis. We introduce random vector fields that share the statistical i ...

SIAM2010

Invariances, Laplacian-Like Wavelet Bases, and the Whitening of Fractal Processes

Michaël Unser, Dimitri Nestor Alice Van De Ville, Pouya Dehghani Tafti

In this contribution, we study the notion of affine invariance (specifically, invariance to the shifting, scaling, and rotation of the coordinate system) as a starting point for the development of mathematical tools and approaches useful in the characteriz ...

IEEE2009

Fractional Laplacian Pyramids

Michaël Unser, Pouya Dehghani Tafti, Ricard Delgado Gonzalo

We provide an extension of the L-2-spline pyramid (Unser et al., 1993) using polyharmonic splines. We analytically prove that the corresponding error pyramid behaves exactly as a multi-scale Laplace operator. We use the multiresolution properties of polyha ...

Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa2009

Self-Similar Random Vector Fields and Their Wavelet Analysis

Michaël Unser, Pouya Dehghani Tafti

This paper is concerned with the mathematical characterization and wavelet analysis of self-similar random vector fields. The study consists of two main parts: the construction of random vector models on the basis of their invariance under coordinate trans ...

SPIE2009

Automatic Tonal Harmonization For Multi-Spectral Mosaics

Pouya Dehghani Tafti

When producing a mosaic of multiple multi-spectral images one needs to harmonize the colours so that the tone transition is smooth from one image to the other. Given two images Im(a) and Im(b), a transform T is sought to map Im(b) to an image that is harmo ...

Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa2008

Innovation modelling and wavelet analysis of fractal processes in bio-imaging

Michaël Unser, Dimitri Nestor Alice Van De Ville, Pouya Dehghani Tafti

Growth and form in biology are often associated with some level of fractality. Fractal characteristics have also been noted in a number of imaging modalities. These observations make fractal modelling relevant in the context of bio-imaging. ...

Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa2008

On Interpolation and Resampling of Discrete Data

Pouya Dehghani Tafti

This letter introduces a new representation of discrete signals based on the mathematical notions of functionals and continuous dual spaces. A new and more general sampling theorem is also suggested. Next, the problems of interpolating and resampling discr ...

IEEE Institute of Electrical and Electronics Engineers2006