44,233 research outputs found
Ionization Electron Signal Processing in Single Phase LArTPCs I. Algorithm Description and Quantitative Evaluation with MicroBooNE Simulation
We describe the concept and procedure of drifted-charge extraction developed
in the MicroBooNE experiment, a single-phase liquid argon time projection
chamber (LArTPC). This technique converts the raw digitized TPC waveform to the
number of ionization electrons passing through a wire plane at a given time. A
robust recovery of the number of ionization electrons from both induction and
collection anode wire planes will augment the 3D reconstruction, and is
particularly important for tomographic reconstruction algorithms. A number of
building blocks of the overall procedure are described. The performance of the
signal processing is quantitatively evaluated by comparing extracted charge
with the true charge through a detailed TPC detector simulation taking into
account position-dependent induced current inside a single wire region and
across multiple wires. Some areas for further improvement of the performance of
the charge extraction procedure are also discussed.Comment: 60 pages, 36 figures. The second part of this work can be found at
arXiv:1804.0258
Construction of Hilbert Transform Pairs of Wavelet Bases and Gabor-like Transforms
We propose a novel method for constructing Hilbert transform (HT) pairs of
wavelet bases based on a fundamental approximation-theoretic characterization
of scaling functions--the B-spline factorization theorem. In particular,
starting from well-localized scaling functions, we construct HT pairs of
biorthogonal wavelet bases of L^2(R) by relating the corresponding wavelet
filters via a discrete form of the continuous HT filter. As a concrete
application of this methodology, we identify HT pairs of spline wavelets of a
specific flavor, which are then combined to realize a family of complex
wavelets that resemble the optimally-localized Gabor function for sufficiently
large orders.
Analytic wavelets, derived from the complexification of HT wavelet pairs,
exhibit a one-sided spectrum. Based on the tensor-product of such analytic
wavelets, and, in effect, by appropriately combining four separable
biorthogonal wavelet bases of L^2(R^2), we then discuss a methodology for
constructing 2D directional-selective complex wavelets. In particular,
analogous to the HT correspondence between the components of the 1D
counterpart, we relate the real and imaginary components of these complex
wavelets using a multi-dimensional extension of the HT--the directional HT.
Next, we construct a family of complex spline wavelets that resemble the
directional Gabor functions proposed by Daugman. Finally, we present an
efficient FFT-based filterbank algorithm for implementing the associated
complex wavelet transform.Comment: 36 pages, 8 figure
Deformable kernels for early vision
Early vision algorithms often have a first stage of linear-filtering that `extracts' from the image information at multiple scales of resolution and multiple orientations. A common difficulty in the design and implementation of such schemes is that one feels compelled to discretize coarsely the space of scales and orientations in order to reduce computation and storage costs. A technique is presented that allows: 1) computing the best approximation of a given family using linear combinations of a small number of `basis' functions; and 2) describing all finite-dimensional families, i.e., the families of filters for which a finite dimensional representation is possible with no error. The technique is based on singular value decomposition and may be applied to generating filters in arbitrary dimensions and subject to arbitrary deformations. The relevant functional analysis results are reviewed and precise conditions for the decomposition to be feasible are stated. Experimental results are presented that demonstrate the applicability of the technique to generating multiorientation multi-scale 2D edge-detection kernels. The implementation issues are also discussed
Efficient reconstruction of band-limited sequences from nonuniformly decimated versions by use of polyphase filter banks
An efficient polyphase structure for the reconstruction of a band-limited sequence from a nonuniformly decimated version is developed. Theoretically, the reconstruction involves the implementation of a bank of multilevel filters, and it is shown that how all these reconstruction filters can be obtained at the cost of one Mth band low-pass filter and a constant matrix multiplier. The resulting structure is therefore more general than previous schemes. In addition, the method offers a direct means of controlling the overall reconstruction distortion T(z) by appropriate design of a low-pass prototype filter P(z). Extension of these results to multiband band-limited signals and to the case of nonconsecutive nonuniform subsampling are also summarized, along with generalizations to the multidimensional case. Design examples are included to demonstrate the theory, and the complexity of the new method is seen to be much lower than earlier ones
A pseudo-matched filter for chaos
A matched filter maximizes the signal-to-noise ratio of a signal. In the
recent work of Corron et al. [Chaos 20, 023123 (2010)], a matched filter is
derived for the chaotic waveforms produced by a piecewise-linear system.
Motivated by these results, we describe a pseudo-matched filter, which removes
noise from the same chaotic signal. It consists of a notch filter followed by a
first-order, low-pass filter. We compare quantitatively the matched filter's
performance to that of our pseudo-matched filter using correlation functions in
a simulated radar application. On average, the pseudo-matched filter performs
with a correlation signal-to-noise ratio that is 2.0 dB below that of the
matched filter. Our pseudo-matched filter, though somewhat inferior in
comparison to the matched filter, is easily realizable at high speed (> 1 GHz)
for potential radar applications
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