Bispectral reconstruction of speckle-degraded images

The bispectrum of a signal has useful properties such as being zero for a Gaussian random process, retaining both phase and magnitude information of the Fourier transform of a signal, and being insensitive to linear motion. It has found applications in a wide variety of fields. The use of these properties for reducing speckle in coherent imaging systems was investigated. It was found that the bispectrum could be used to restore speckle-degraded images. Coherent speckle noise is modeled as a multiplicative noise process. By using a logarithmic transformation, this speckle noise is converted to a signal independent, additive process which is close to Gaussian when an integrating aperture is used. Bispectral reconstruction of speckle-degraded images is performed on such logarithmically transformed images when we have independent multiple snapshots

Propriétés des processus H-ARMA

Nous introduisons une nouvelle classe de modèles non gaussiens appelés H-ARMA qui sont obtenus par filtrage non linéaire d'une entrée gaussienne colorée. La structure non linéaire constituée de polynômes d'Hermite permet non seulement de couvrir une large plage de comportements non gaussiens, mais surtout d'obtenir des résultats analytiques sur les comportements probabilistes et statistiques des modèles H-ARMA. Ces résultats théoriques sont une bonne base pour l'étude complète de ces modèles et en particulier leur identification

The Interplay of Architecture and Correlated Variability in Neuronal Networks

This much is certain: neurons are coupled, and they exhibit covariations in their output. The extent of each does not have a single answer. Moreover, the strength of neuronal correlations, in particular, has been a subject of hot debate within the neuroscience community over the past decade, as advancing recording techniques have made available a lot of new, sometimes seemingly conflicting, datasets. The impact of connectivity and the resulting correlations on the ability of animals to perform necessary tasks is even less well understood. In order to answer relevant questions in these categories, novel approaches must be developed. This work focuses on three somewhat distinct, but inseparably coupled, crucial avenues of research within the broader field of computational neuroscience. First, there is a need for tools which can be applied, both by experimentalists and theorists, to understand how networks transform their inputs. In turn, these tools will allow neuroscientists to tease apart the structure which underlies network activity. The Generalized Thinning and Shift framework, presented in Chapter 4, addresses this need. Next, taking for granted a general understanding of network architecture as well as some grasp of the behavior of its individual units, we must be able to reverse the activity to structure relationship, and understand instead how network structure determines dynamics. We achieve this in Chapters 5 through 7 where we present an application of linear response theory yielding an explicit approximation of correlations in integrate--and--fire neuronal networks. This approximation reveals the explicit relationship between correlations, structure, and marginal dynamics. Finally, we must strive to understand the functional impact of network dynamics and architecture on the tasks that a neural network performs. This need motivates our analysis of a biophysically detailed model of the blow fly visual system in Chapter 8. Our hope is that the work presented here represents significant advances in multiple directions within the field of computational neuroscience.Mathematics, Department o