902 research outputs found
Nonlinear Channel Estimation for OFDM System by Complex LS-SVM under High Mobility Conditions
A nonlinear channel estimator using complex Least Square Support Vector
Machines (LS-SVM) is proposed for pilot-aided OFDM system and applied to Long
Term Evolution (LTE) downlink under high mobility conditions. The estimation
algorithm makes use of the reference signals to estimate the total frequency
response of the highly selective multipath channel in the presence of
non-Gaussian impulse noise interfering with pilot signals. Thus, the algorithm
maps trained data into a high dimensional feature space and uses the structural
risk minimization (SRM) principle to carry out the regression estimation for
the frequency response function of the highly selective channel. The
simulations show the effectiveness of the proposed method which has good
performance and high precision to track the variations of the fading channels
compared to the conventional LS method and it is robust at high speed mobility.Comment: 11 page
Parallel Magnetic Resonance Imaging as Approximation in a Reproducing Kernel Hilbert Space
In Magnetic Resonance Imaging (MRI) data samples are collected in the spatial
frequency domain (k-space), typically by time-consuming line-by-line scanning
on a Cartesian grid. Scans can be accelerated by simultaneous acquisition of
data using multiple receivers (parallel imaging), and by using more efficient
non-Cartesian sampling schemes. As shown here, reconstruction from samples at
arbitrary locations can be understood as approximation of vector-valued
functions from the acquired samples and formulated using a Reproducing Kernel
Hilbert Space (RKHS) with a matrix-valued kernel defined by the spatial
sensitivities of the receive coils. This establishes a formal connection
between approximation theory and parallel imaging. Theoretical tools from
approximation theory can then be used to understand reconstruction in k-space
and to extend the analysis of the effects of samples selection beyond the
traditional g-factor noise analysis to both noise amplification and
approximation errors. This is demonstrated with numerical examples.Comment: 28 pages, 7 figure
Continuous-Domain Solutions of Linear Inverse Problems with Tikhonov vs. Generalized TV Regularization
We consider linear inverse problems that are formulated in the continuous
domain. The object of recovery is a function that is assumed to minimize a
convex objective functional. The solutions are constrained by imposing a
continuous-domain regularization. We derive the parametric form of the solution
(representer theorems) for Tikhonov (quadratic) and generalized total-variation
(gTV) regularizations. We show that, in both cases, the solutions are splines
that are intimately related to the regularization operator. In the Tikhonov
case, the solution is smooth and constrained to live in a fixed subspace that
depends on the measurement operator. By contrast, the gTV regularization
results in a sparse solution composed of only a few dictionary elements that
are upper-bounded by the number of measurements and independent of the
measurement operator. Our findings for the gTV regularization resonates with
the minimization of the norm, which is its discrete counterpart and also
produces sparse solutions. Finally, we find the experimental solutions for some
measurement models in one dimension. We discuss the special case when the gTV
regularization results in multiple solutions and devise an algorithm to find an
extreme point of the solution set which is guaranteed to be sparse
Signal Reconstruction From Nonuniform Samples Using Prolate Spheroidal Wave Functions: Theory and Application
Nonuniform sampling occurs in many applications due to imperfect sensors, mismatchedclocks or event-triggered phenomena. Indeed, natural images, biomedical responses andsensor network transmission have bursty structure so in order to obtain samples that correspondto the information content of the signal, one needs to collect more samples when thesignal changes fast and fewer samples otherwise which creates nonuniformly distibuted samples.On the other hand, with the advancements in the integrated circuit technology, smallscale and ultra low-power devices are available for several applications ranging from invasivebiomedical implants to environmental monitoring. However the advancements in the devicetechnologies also require data acquisition methods to be changed from the uniform (clockbased, synchronous) to nonuniform (clockless, asynchronous) processing. An important advancementis in the data reconstruction theorems from sub-Nyquist rate samples which wasrecently introduced as compressive sensing and that redenes the uncertainty principle. Inthis dissertation, we considered the problem of signal reconstruction from nonuniform samples.Our method is based on the Prolate Spheroidal Wave Functions (PSWF) which can beused in the reconstruction of time-limited and essentially band-limited signals from missingsamples, in event-driven sampling and in the case of asynchronous sigma delta modulation.We provide an implementable, general reconstruction framework for the issues relatedto reduction in the number of samples and estimation of nonuniform sample times. We alsoprovide a reconstruction method for level crossing sampling with regularization. Another way is to use projection onto convex sets (POCS) method. In this method we combinea time-frequency approach with the POCS iterative method and use PSWF for the reconstructionwhen there are missing samples. Additionally, we realize time decoding modulationfor an asynchronous sigma delta modulator which has potential applications in low-powerbiomedical implants
Sampling based on timing: Time encoding machines on shift-invariant subspaces
Sampling information using timing is a new approach in sampling theory. The
question is how to map amplitude information into the timing domain. One such
encoder, called time encoding machine, was introduced by Lazar and Toth in [23]
for the special case of band-limited functions. In this paper, we extend their
result to the general framework of shift-invariant subspaces. We prove that
time encoding machines may be considered as non-uniform sampling devices, where
time locations are unknown a priori. Using this fact, we show that perfect
representation and reconstruction of a signal with a time encoding machine is
possible whenever this device satisfies some density property. We prove that
this method is robust under timing quantization, and therefore can lead to the
design of simple and energy efficient sampling devices.Comment: submitted to Applied and Computationnal Harmonic Analysi
Sparse deconvolution using support vector machines
Sparse deconvolution is a classical subject in digital signal processing, having many practical applications. Support vector machine (SVM) algorithms show a series of characteristics, such as sparse solutions and implicit regularization, which make them attractive for solving sparse deconvolution problems. Here, a sparse deconvolution algorithm based on the SVM framework for signal processing is presented and analyzed, including comparative evaluations of its performance from the points of view of estimation and detection capabilities, and of robustness with respect to non-Gaussian additive noise.Publicad
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