142 research outputs found
Low-Floor Tanner Codes via Hamming-Node or RSCC-Node Doping
We study the design of structured Tanner codes with low error-rate floors on the AWGN channel. The design technique involves the “doping” of standard LDPC (proto-)graphs, by which we mean Hamming or recursive systematic convolutional (RSC) code constraints are used together with single-parity-check (SPC) constraints to construct a code’s protograph. We show that the doping of a “good” graph with Hamming or RSC codes is a pragmatic approach that frequently results in a code with a good threshold and very low error-rate floor. We focus on low-rate Tanner codes, in part because the design of low-rate, low-floor LDPC codes is particularly difficult. Lastly, we perform a simple complexity analysis of our Tanner codes and examine the performance of lower-complexity, suboptimal Hamming-node decoders
Identification-detection group testing protocols for COVID-19 at high prevalence
Group testing allows saving chemical reagents, analysis time, and costs, by testing pools of samples instead of individual samples. We introduce a class of group testing protocols with small dilution, suited to operate even at high prevalence (5–10%), and maximizing the fraction of samples classified positive/negative within the first round of tests. Precisely, if the tested group has exactly one positive sample then the protocols identify it without further individual tests. The protocols also detect the presence of two or more positives in the group, in which case a second round could be applied to identify the positive individuals. With a prevalence of 5 % and maximum dilution 6, with 100 tests we classify 242 individuals, 92 % of them in one round and 8 % requiring a second individual test. In comparison, the Dorfman’s scheme can test 229 individuals with 100 tests, with a second round for 18.5 % of the individuals
High Resolution 3D Ultrasonic Breast Imaging by Time-Domain Full Waveform Inversion
Ultrasound tomography (UST) scanners allow quantitative images of the human
breast's acoustic properties to be derived with potential applications in
screening, diagnosis and therapy planning. Time domain full waveform inversion
(TD-FWI) is a promising UST image formation technique that fits the parameter
fields of a wave physics model by gradient-based optimization. For high
resolution 3D UST, it holds three key challenges: Firstly, its central building
block, the computation of the gradient for a single US measurement, has a
restrictively large memory footprint. Secondly, this building block needs to be
computed for each of the measurements, resulting in a massive
parallel computation usually performed on large computational clusters for
days. Lastly, the structure of the underlying optimization problem may result
in slow progression of the solver and convergence to a local minimum. In this
work, we design and evaluate a comprehensive computational strategy to overcome
these challenges: Firstly, we introduce a novel gradient computation based on
time reversal that dramatically reduces the memory footprint at the expense of
one additional wave simulation per source. Secondly, we break the dependence on
the number of measurements by using source encoding (SE) to compute stochastic
gradient estimates. Also we describe a more accurate, TD-specific SE technique
with a finer variance control and use a state-of-the-art stochastic LBFGS
method. Lastly, we design an efficient TD multi-grid scheme together with
preconditioning to speed up the convergence while avoiding local minima. All
components are evaluated in extensive numerical proof-of-concept studies
simulating a bowl-shaped 3D UST breast scanner prototype. Finally, we
demonstrate that their combination allows us to obtain an accurate 442x442x222
voxel image with a resolution of 0.5mm using Matlab on a single GPU within 24h
Time domain reconstruction of sound speed and attenuation in ultrasound computed tomography using full wave inversion
Ultrasound computed tomography (USCT) is a non-invasive imaging technique that provides information
about the acoustic properties of soft tissues in the body, such as the speed of sound (SS) and
acoustic attenuation (AA). Knowledge of these properties can improve the discrimination between
benign and malignant masses, especially in breast cancer studies. Full wave inversion (FWI) methods
for image reconstruction in USCT provide the best image quality compared to more approximate
methods. Using FWI, the SS is usually recovered in the time domain, and the AA is usually
recovered in the frequency domain. Nevertheless, as both properties can be obtained from the same
data, it is desirable to have a common framework to reconstruct both distributions. In this work, an
algorithm is proposed to reconstruct both the SS and AA distributions using a time domain FWI
methodology based on the fractional Laplacian wave equation, an adjoint field formulation, and a
gradient-descent method. The optimization code employs a Compute Unified Device Architecture
version of the software k-Wave, which provides high computational efficiency. The performance of
the method was evaluated using simulated noisy data from numerical breast phantoms. Errors were
less than 0.5% in the recovered SS and 10% in the AA. V
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