15 research outputs found
Innovation Rate Sampling of Pulse Streams with Application to Ultrasound Imaging
Signals comprised of a stream of short pulses appear in many applications
including bio-imaging and radar. The recent finite rate of innovation
framework, has paved the way to low rate sampling of such pulses by noticing
that only a small number of parameters per unit time are needed to fully
describe these signals. Unfortunately, for high rates of innovation, existing
sampling schemes are numerically unstable. In this paper we propose a general
sampling approach which leads to stable recovery even in the presence of many
pulses. We begin by deriving a condition on the sampling kernel which allows
perfect reconstruction of periodic streams from the minimal number of samples.
We then design a compactly supported class of filters, satisfying this
condition. The periodic solution is extended to finite and infinite streams,
and is shown to be numerically stable even for a large number of pulses. High
noise robustness is also demonstrated when the delays are sufficiently
separated. Finally, we process ultrasound imaging data using our techniques,
and show that substantial rate reduction with respect to traditional ultrasound
sampling schemes can be achieved.Comment: 14 pages, 13 figure
Exact and approximate Strang-Fix conditions to reconstruct signals with finite rate of innovation from samples taken with arbitrary kernels
In the last few years, several new methods have been developed for the sampling and
exact reconstruction of specific classes of non-bandlimited signals known as signals with finite rate of innovation (FRI). This is achieved by using adequate sampling kernels and
reconstruction schemes. An example of valid kernels, which we use throughout the thesis,
is given by the family of exponential reproducing functions. These satisfy the generalised
Strang-Fix conditions, which ensure that proper linear combinations of the kernel with its
shifted versions reproduce polynomials or exponentials exactly.
The first contribution of the thesis is to analyse the behaviour of these kernels in the
case of noisy measurements in order to provide clear guidelines on how to choose the exponential
reproducing kernel that leads to the most stable reconstruction when estimating
FRI signals from noisy samples. We then depart from the situation in which we can choose
the sampling kernel and develop a new strategy that is universal in that it works with any
kernel. We do so by noting that meeting the exact exponential reproduction condition is
too stringent a constraint. We thus allow for a controlled error in the reproduction formula
in order to use the exponential reproduction idea with arbitrary kernels and develop
a universal reconstruction method which is stable and robust to noise.
Numerical results validate the various contributions of the thesis and in particular show
that the approximate exponential reproduction strategy leads to more stable and accurate
reconstruction results than those obtained when using the exact recovery methods.Open Acces
Feature Extraction for image super-resolution using finite rate of innovation principles
To understand a real-world scene from several multiview pictures, it is necessary to find
the disparities existing between each pair of images so that they are correctly related to one
another. This process, called image registration, requires the extraction of some specific
information about the scene. This is achieved by taking features out of the acquired
images. Thus, the quality of the registration depends largely on the accuracy of the
extracted features.
Feature extraction can be formulated as a sampling problem for which perfect re-
construction of the desired features is wanted. The recent sampling theory for signals with
finite rate of innovation (FRI) and the B-spline theory offer an appropriate new frame-
work for the extraction of features in real images. This thesis first focuses on extending the
sampling theory for FRI signals to a multichannel case and then presents exact sampling
results for two different types of image features used for registration: moments and edges.
In the first part, it is shown that the geometric moments of an observed scene can
be retrieved exactly from sampled images and used as global features for registration. The
second part describes how edges can also be retrieved perfectly from sampled images for
registration purposes. The proposed feature extraction schemes therefore allow in theory
the exact registration of images. Indeed, various simulations show that the proposed
extraction/registration methods overcome traditional ones, especially at low-resolution.
These characteristics make such feature extraction techniques very appropriate for
applications like image super-resolution for which a very precise registration is needed. The
quality of the super-resolved images obtained using the proposed feature extraction meth-
ods is improved by comparison with other approaches. Finally, the notion of polyphase
components is used to adapt the image acquisition model to the characteristics of real
digital cameras in order to run super-resolution experiments on real images
Exact Local Reconstruction Algorithms for Signals with Finite Rate of Innovation
Consider the problem of sampling signals which are not bandlimited, but still have a finite number of degrees of freedom per unit of time, such as, for example, piecewise polynomial or piecewise sinusoidal signals, and call the number of degrees of freedom per unit of time the rate of innovation. Classical sampling theory does not enable a perfect reconstruction of such signals since they are not bandlimited. In this paper, we show that many signals with finite rate of innovation can be sampled and perfectly reconstructed using kernels of compact support and a local reconstruction algorithm. The class of kernels that we can use is very rich and includes functions satisfying strang-fix conditions, exponential splines and functions with rational Fourier transforms. Extension of such results to the 2-dimensional case are also discussed and an application to image super-resolution is presente
Feature Extraction for Image Super-resolution using Finite Rate of Innovation Principles
To understand a real-world scene from several multiview pictures, it is necessary to find the disparities existing between each pair of images so that they are correctly related to one another., This process. called image registration, reguires the extraction of some specific information about the scene. This is achieved by taking features out of the acquired imaqes. Thus, the quality of the, registration depends largely on the accuracy of the extracted features. Feature extraction can be formulated as a sampling problem for which perfect reconstruction of the, desired features is wanted. The recent sampling theory for signals with finite rate of innovation (FR/), and the B-spline theory offer an appropriate new framework for the extraction of features in real, images. This thesis first focuses on extending the sampling theory for FRI signals to a multichannel, case and then presents exact sampling results for two different types of image features used for, registration: moments and edges. In the first part, it is shown that the geometric moments of an observed scene can be retrieved exactly from sampled images and used as global features for registration. The second part describes how edges can also be retrieved perfectly from sampled images for registration purposes. The proposed feature extraction schemes therefore allow in theory the exact registration of images. Indeed, various simulations show that the proposed extraction/registration methods overcome traditional ones, especially at low-resolution. These characteristics make such feature extraction techniques very appropriate for applications like image super-resolution for which a very precise registration is needed. The quality of the superresolved images obtained using the proposed feature extraction methods is improved by comparison with other approaches. Finally, the notion of polyphase components is used to adapt the imaqe acquisition model to the characteristics of real digital cameras in order to run super-resolution experiments on real images