Identification of defective members of large populations has been widely studied in the statistic... more Identification of defective members of large populations has been widely studied in the statistics community under the name of group testing. It involves grouping subsets of items into different pools and detecting defective members based on the set of test results obtained for each pool. In a classical noiseless group testing setup, it is assumed that the sampling procedure is
Recent advances in associative memory design through strutured pattern sets and graph-based infer... more Recent advances in associative memory design through strutured pattern sets and graph-based inference algorithms have allowed the reliable learning and retrieval of an exponential number of patterns. Both these and classical associative memories, however, have assumed internally noiseless computational nodes. This paper considers the setting when internal computations are also noisy. Even if all components are noisy, the final error probability in recall can often be made exceedingly small, as we characterize. There is a threshold phenomenon. We also show how to optimize inference algorithm parameters when knowing statistical properties of internal noise.
Calibration of ultrasound tomography devices is a challenging problem and of highly practical int... more Calibration of ultrasound tomography devices is a challenging problem and of highly practical interest in medical and seismic imaging. This work addresses the position calibration problem in circular apertures where sensors are arranged on a circular ring and act both as transmitters and receivers.We introduce a new method of calibration based on the time-of-flight (ToF) measurements between sensors when the enclosed medium is homogeneous. Knowing all the pairwise ToFs, one can find the positions of the sensors using multi-dimensional scaling (MDS) method. In practice, however, we are facing two major sources of loss. One is due to the transitional behaviour of the sensors, which makes the ToF measurements for close-by sensors unavailable. The other is due to the random malfunctioning of the sensors, that leads to random missing ToF measurements. On top of the missing entries, since in practice the impulse response of the piezoelectric and the time origin in the measurement procedur...
We study the calibration problem in circular ultrasound tomography devices for breast imaging, wh... more We study the calibration problem in circular ultrasound tomography devices for breast imaging, where the sensor positions deviate from the circumference of a perfect circle. We introduce a new method of calibration based on the time-of-flight (ToF) measurements between sensors when the enclosed medium is homogeneous. In the presence of all the pairwise ToFs, one can estimate the sensor positions using multi-dimensional scaling (MDS) method. In practice, however, we are facing two major sources of loss. One is due to the transitional behaviour of the sensors and the beam form of the transducers, which makes the ToF measurements for close-by sensors unavailable. The other is due to the random malfunctioning of the sensors, that leads to random missing ToF measurements. On top of the missing entries, in practice an unknown time delay is also added to the measurements. In this work, we show that a matrix defined from all the ToF measurements is of rank at most four. In order to estimate...
Compressed sensing deals with the reconstruction of sparse signals using a small number of linear... more Compressed sensing deals with the reconstruction of sparse signals using a small number of linear measurements. One of the main challenges in compressed sensing is to find the support of a sparse signal. In the literature, several bounds on the scaling law of the number of measurements for successful support recovery have been derived where the main focus is on random Gaussian measurement matrices. In this paper, we investigate the noisy support recovery problem from an estimation theoretic point of view, where no specific assumption is made on the underlying measurement matrix. The linear measurements are perturbed by additive white Gaussian noise. We define the output of a support estimator to be a set of position values in increasing order. We set the error between the true and estimated supports as the $\ell_2$-norm of their difference. On the one hand, this choice allows us to use the machinery behind the $\ell_2$-norm error metric and on the other hand, converts the support re...
2012 IEEE International Symposium on Information Theory Proceedings, 2012
ABSTRACT The problem of neural network association is to retrieve a previously memorized pattern ... more ABSTRACT The problem of neural network association is to retrieve a previously memorized pattern from its noisy version using a network of neurons. An ideal neural network should include three components simultaneously: a learning algorithm, a large pattern retrieval capacity and resilience against noise. Prior works in this area usually improve one or two aspects at the cost of the third. Our work takes a step forward in closing this gap. More specifically, we show that by forcing natural constraints on the set of learning patterns, we can drastically improve the retrieval capacity of our neural network. Moreover, we devise a learning algorithm whose role is to learn those patterns satisfying the above mentioned constraints. Finally we show that our neural network can cope with a fair amount of noise.
ABSTRACT In conventional group testing, the goal is to detect a small subset of defecting items D... more ABSTRACT In conventional group testing, the goal is to detect a small subset of defecting items D in a large population N by grouping arbitrary subset of N into different pools. The result of each group test T is a binary output depending on whether the group contains a defective item or not. The main challenge is to minimize the number of pools required to identify the set D. Motivated by applications in network monitoring and infection propagation, we consider the problem of group testing with graph constraints. As opposed to conventional group testing where any subset of items can be pooled, here a test is admissible if it induces a connected subgraph H ⊂ G. In contrast to the non-adaptive pooling process used in previous work, we first show that by exploiting an adaptive strategy, one can dramatically reduce the number of tests. More specifically, for any graph G, we devise a 2-approximation algorithm (and hence order optimal) that locates the set of defective items D. To obtain a good compromise between adaptive and non-adaptive strategies, we then devise a multi-stage algorithm. In particular, we show that if the set of defective items are uniformly distributed, then an l-stage pooling strategy can identify the defective set in O(l·|D|·|N|1/l) tests, on the average. In particular, for l = log(|N|) stages, the number of tests reduces to 4|D| log(|N|), which in turn is order optimum.
Identification of defective members of large populations has been widely studied in the statistic... more Identification of defective members of large populations has been widely studied in the statistics community under the name of group testing. It involves grouping subsets of items into different pools and detecting defective members based on the set of test results obtained for each pool. In a classical noiseless group testing setup, it is assumed that the sampling procedure is
Recent advances in associative memory design through strutured pattern sets and graph-based infer... more Recent advances in associative memory design through strutured pattern sets and graph-based inference algorithms have allowed the reliable learning and retrieval of an exponential number of patterns. Both these and classical associative memories, however, have assumed internally noiseless computational nodes. This paper considers the setting when internal computations are also noisy. Even if all components are noisy, the final error probability in recall can often be made exceedingly small, as we characterize. There is a threshold phenomenon. We also show how to optimize inference algorithm parameters when knowing statistical properties of internal noise.
Calibration of ultrasound tomography devices is a challenging problem and of highly practical int... more Calibration of ultrasound tomography devices is a challenging problem and of highly practical interest in medical and seismic imaging. This work addresses the position calibration problem in circular apertures where sensors are arranged on a circular ring and act both as transmitters and receivers.We introduce a new method of calibration based on the time-of-flight (ToF) measurements between sensors when the enclosed medium is homogeneous. Knowing all the pairwise ToFs, one can find the positions of the sensors using multi-dimensional scaling (MDS) method. In practice, however, we are facing two major sources of loss. One is due to the transitional behaviour of the sensors, which makes the ToF measurements for close-by sensors unavailable. The other is due to the random malfunctioning of the sensors, that leads to random missing ToF measurements. On top of the missing entries, since in practice the impulse response of the piezoelectric and the time origin in the measurement procedur...
We study the calibration problem in circular ultrasound tomography devices for breast imaging, wh... more We study the calibration problem in circular ultrasound tomography devices for breast imaging, where the sensor positions deviate from the circumference of a perfect circle. We introduce a new method of calibration based on the time-of-flight (ToF) measurements between sensors when the enclosed medium is homogeneous. In the presence of all the pairwise ToFs, one can estimate the sensor positions using multi-dimensional scaling (MDS) method. In practice, however, we are facing two major sources of loss. One is due to the transitional behaviour of the sensors and the beam form of the transducers, which makes the ToF measurements for close-by sensors unavailable. The other is due to the random malfunctioning of the sensors, that leads to random missing ToF measurements. On top of the missing entries, in practice an unknown time delay is also added to the measurements. In this work, we show that a matrix defined from all the ToF measurements is of rank at most four. In order to estimate...
Compressed sensing deals with the reconstruction of sparse signals using a small number of linear... more Compressed sensing deals with the reconstruction of sparse signals using a small number of linear measurements. One of the main challenges in compressed sensing is to find the support of a sparse signal. In the literature, several bounds on the scaling law of the number of measurements for successful support recovery have been derived where the main focus is on random Gaussian measurement matrices. In this paper, we investigate the noisy support recovery problem from an estimation theoretic point of view, where no specific assumption is made on the underlying measurement matrix. The linear measurements are perturbed by additive white Gaussian noise. We define the output of a support estimator to be a set of position values in increasing order. We set the error between the true and estimated supports as the $\ell_2$-norm of their difference. On the one hand, this choice allows us to use the machinery behind the $\ell_2$-norm error metric and on the other hand, converts the support re...
2012 IEEE International Symposium on Information Theory Proceedings, 2012
ABSTRACT The problem of neural network association is to retrieve a previously memorized pattern ... more ABSTRACT The problem of neural network association is to retrieve a previously memorized pattern from its noisy version using a network of neurons. An ideal neural network should include three components simultaneously: a learning algorithm, a large pattern retrieval capacity and resilience against noise. Prior works in this area usually improve one or two aspects at the cost of the third. Our work takes a step forward in closing this gap. More specifically, we show that by forcing natural constraints on the set of learning patterns, we can drastically improve the retrieval capacity of our neural network. Moreover, we devise a learning algorithm whose role is to learn those patterns satisfying the above mentioned constraints. Finally we show that our neural network can cope with a fair amount of noise.
ABSTRACT In conventional group testing, the goal is to detect a small subset of defecting items D... more ABSTRACT In conventional group testing, the goal is to detect a small subset of defecting items D in a large population N by grouping arbitrary subset of N into different pools. The result of each group test T is a binary output depending on whether the group contains a defective item or not. The main challenge is to minimize the number of pools required to identify the set D. Motivated by applications in network monitoring and infection propagation, we consider the problem of group testing with graph constraints. As opposed to conventional group testing where any subset of items can be pooled, here a test is admissible if it induces a connected subgraph H ⊂ G. In contrast to the non-adaptive pooling process used in previous work, we first show that by exploiting an adaptive strategy, one can dramatically reduce the number of tests. More specifically, for any graph G, we devise a 2-approximation algorithm (and hence order optimal) that locates the set of defective items D. To obtain a good compromise between adaptive and non-adaptive strategies, we then devise a multi-stage algorithm. In particular, we show that if the set of defective items are uniformly distributed, then an l-stage pooling strategy can identify the defective set in O(l·|D|·|N|1/l) tests, on the average. In particular, for l = log(|N|) stages, the number of tests reduces to 4|D| log(|N|), which in turn is order optimum.
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Papers by Amin Karbasi