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- Michael Unser, Pouya Dehghani Tafti, Arash Amini, Hagai Kirshner
- ArXiv
- 2011

This paper is devoted to the characterization of an extended family of CARMA (continuous-time autoregressive moving average) processes that are solutions of stochastic differential equations driven by white Lévy innovations. These are completely specified by: (1) a set of poles and zeros that fixes their correlation structure, and (2) a canonical… (More)

- Michael Unser, Pouya Dehghani Tafti, Qiyu Sun
- ArXiv
- 2011

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 white noise process, which may be Gaussian or not (e.g., Laplace, impulsive Poisson or alpha stable).… (More)

- Michael Unser, Pouya Dehghani Tafti, Qiyu Sun
- IEEE Trans. Information Theory
- 2014

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 white noise process, which may be Gaussian or not (e.g., Laplace, impulsive Poisson, or alpha stable).… (More)

- Pouya Dehghani Tafti, Michael Unser
- IEEE Transactions on Image Processing
- 2011

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 coordinate system. In preparation for our general result, we also address some commonalities of invariant… (More)

- Michael Unser, Pouya Dehghani Tafti, Arash Amini, Hagai Kirshner
- IEEE Trans. Information Theory
- 2014

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 Lévy innovations. These are completely specified by: 1) a set of poles and zeros that fixes their correlation structure and 2) a canonical infinitely… (More)

- Pouya Dehghani Tafti, Michael Unser
- Multiscale Modeling & Simulation
- 2010

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 invariances of standard vector fBm (self-similarity and rotation invariance) but which, in contrast,… (More)

- Pouya Dehghani Tafti, Shahram Shirani, Xiaolin Wu
- ICASSP
- 2005

- Michael Unser, Pouya Dehghani Tafti
- IEEE Transactions on Signal Processing
- 2011

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 analogous conceptually to the classical interpretation of a Gaussian stationary process as filtered white… (More)

- Pouya Dehghani Tafti, Dimitri Van De Ville, Michael Unser
- IEEE Transactions on Image Processing
- 2009

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 characterization and analysis of multivariate fractional Brownian motion (fBm) fields. In particular, using a… (More)

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 such as curl and divergence. We point out the invariance properties of the scheme with respect to… (More)