Filtre numérique | EPFL Graph Search

En électronique, un filtre numérique est un élément qui effectue un filtrage à l'aide d'une succession d'opérations mathématiques sur un signal discret. C'est-à-dire qu'il modifie le contenu spectral du signal d'entrée en atténuant ou éliminant certaines composantes spectrales indésirées. Contrairement aux filtres analogiques, qui sont réalisés à l'aide d'un agencement de composantes physiques (résistance, condensateur, inductance, transistor, etc.), les filtres numériques sont réalisés soit par des circuits intégrés dédiés, des processeurs programmables (FPGA, microprocesseur, DSP, microcontrôleur, etc.), soit par logiciel dans un ordinateur. Les filtres numériques peuvent, en théorie, réaliser la totalité des effets de filtrage pouvant être définis par des fonctions mathématiques ou des algorithmes. Les deux principales limitations des filtres numériques sont la vitesse et le coût. La vitesse du filtre est limitée par la vitesse (l'horloge, le « clock » en anglais) du processeu

Nondyadic and nonlinear multiresolution image approximations

Maria Arrate Munoz Barrutia

This thesis focuses on the development of novel multiresolution image approximations. Specifically, we present two kinds of generalization of multiresolution techniques: image reduction for arbitrary scales, and nonlinear approximations using other metrics than the standard Euclidean one. Traditional multiresolution decompositions are restricted to dyadic scales. As first contribution of this thesis, we develop a method that goes beyond this restriction and that is well suited to arbitrary scale-change computations. The key component is a new and numerically exact algorithm for computing inner products between a continuously defined signal and B-splines of any order and of arbitrary sizes. The technique can also be applied for non-uniform to uniform grid conversion, which is another approximation problem where our method excels. Main applications are resampling and signal reconstruction. Although simple to implement, least-squares approximations lead to artifacts that could be reduced if nonlinear methods would be used instead. The second contribution of the thesis is the development of nonlinear spline pyramids that are optimal for lp-norms. First, we introduce a Banach-space formulation of the problem and show that the solution is well defined. Second, we compute the lp-approximation thanks to an iterative optimization algorithm based on digital filtering. We conclude that l1-approximations reduce the artifacts that are inherent to least-squares methods; in particular, edge blurring and ringing. In addition, we observe that the error of l1-approximations is sparser. Finally, we derive an exact formula for the asymptotic Lp-error; this result justifies using the least-squares approximation as initial solution for the iterative optimization algorithm when the degree of the spline is even; otherwise, one has to include an appropriate correction term. The theoretical background of the thesis includes the modelisation of images in a continuous/discrete formalism and takes advantage of the approximation theory of linear shift-invariant operators. We have chosen B-splines as basis functions because of their nice properties. We also propose a new graphical formalism that links B-splines, finite differences, differential operators, and arbitrary scale changes.

EPFL2002

Region Of Interest X-Ray Computed Tomography Via Corrected Back Projection

Michael Thompson McCann, Michaël Unser, Laura Vilaclara

We present a new method for region of interest (ROI) reconstruction from high-resolution, nontruncated data in parallel-ray X-ray computed tomography (CT). Many of the approaches to ROI CT reconstruction in the literature rely on a costly forward projection step to form an ROI-only sinogram. Our approach instead relies on a digital filtering implementation of the normal operator ((HH)-H-T) to compute a back projected version of the ROI-only sinogram that can be used directly for reconstruction, thus eliminating the forward projection step altogether. Results on three synthetic datasets with a variety of experimental conditions show that the method provides accuracy on par with a full reconstruction at a fraction of the time and memory cost.

IEEE2018

Networks of Coupled VO2 Oscillators for Neuromorphic Computing

Elisabetta Corti

Neuromorphic computing is a wide research field aimed to the realization of brain-inspired hardware, apt to tackle computation of unstructured data more efficiently than currently done with standard computational units. Oscillatory neural networks are known for their associative memory capability, which enables to retrieve the information stored in the system from noisy or incomplete data. The development of phase-transition materials such as vanadiumdioxide (VO2) allows to design compact relaxation oscillator units which can be coupled in frequency and phase to realize an oscillatory neural network in hardware. In this thesis, we investigate the oscillatory neural network technology from the realization of the basic oscillator components with VO2 to the exploitation of the coupled oscillators as analog filters in convolutional neural networks applications. VO2 phase-transition devices are realized in a CMOS compatible process in two geometries, a planar and a crossbar configuration. The impact of the polycrystallinity of the VO2 film on the insulator-to-metal transition of the device is analyzed; through the contacting of a single grain we demonstrate the realization of a VO2 device with a single, sharp phase transition. The VO2 devices are connected in circuits to build networks of coupled oscillators. Through coupling with resistive and capacitive elements, experimental demonstrations of a 4-VO2 coupled oscillator network is shown. The network encodes the input and output information in the relative phase of the oscillators. The associative memory capability of the system is used to extract features from hand-written digits. By expanding the network to a 3×3 coupled oscillator system, we demonstrate in simulations how an oscillatory neural network can replace up to five digital filters in a convolutional neural network, retaining the same image processing capabilities.

EPFL2021

Nondyadic and nonlinear multiresolution image approximations

Maria Arrate Munoz Barrutia

EPFL2002