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Recovery of sparse signals with unknown clustering pattern in the case of having partial erroneous prior knowledge on the supports of the signal is considered. In this case, we provide a modified sparse Bayesian learning model to incorporate prior knowledge and simultaneously learn the unknown clustering pattern. For this purpose, we add one more layer to support-aided sparse Bayesian learning algorithm...
In this paper, we propose a Bayesian framework for robust Kalman filtering when noise statistics are unknown. The proposed intrinsically Bayesian robust Kalman filter is robust in the Bayesian sense meaning that it guarantees the best average performance relative to the prior distribution governing unknown noise parameters. The basics of Kalman filtering such as the projection theorem and the innovation...
We consider the problem of recovering an image using block compressed sensing (BCS). Traditional BCS algorithms recovers each image block independently and utilizes post-processing methods for removing the blocking artifacts. In contrast, we propose an image recovery method free of post-processing, where we utilize a lapped transform (LT) for the sparse representation of the image in order to reduce...
An exact Bayesian likelihood ratio is derived for detecting the presence of a rank-2 signal in M > 2 channels of noisy receiver data under the assumption that the signal is known to be present on K = 2 of the channels (reference channels). The objective of the test is thus to ascertain whether the signal is also present on the other channels (surveillance channels). The performance of the Bayesian...
The estimation of the Ricean K factor in case of noisy complex channel coefficients is addressed. A new deterministic estimator is designed, and the relevant deterministic Cramer-Rao Lower Bound (CRLB) is derived. It is shown by simulation that the new estimator outperforms the existing ones in term of both bias and Normalized Mean Square Error (NMSE), and is close to the CRLB. We also design two...
Experiments by Ratnam et al.[1] demonstrate the benefit of drift eye movements for the discrimination of a diffraction-limited tumbling E sized near the sampling limit of the cone photoreceptor array. Subjects perform better at discriminating the orientation of the E when its projection moves on the retina with the same motion statistics as drift eye movements, but not necessarily correlated to the...
In soft decoding, log-likelihood ratios (LLRs) are calculated from estimated data symbols. Data symbols from proper constellation diagrams such as QPSK are often estimated using the linear minimum mean square error (LMMSE) estimator. We prove that the recently introduced component-wise conditionally unbiased (CWCU) LMMSE estimator results in the very same LLRs as the LMMSE estimator for typical model...
We investigate the task of model selection for high-dimensional data. For this purpose, we propose an extension to the Bayesian information criterion. Our information criterion is asymptotically consistent either as the number of measurements tends to infinity or as the variance of noise decreases to zero. The numerical results provided support our claim. Additionally, we highlight the link between...
In this paper, decentralized change point detection problem with optional observations at the fusion center is considered. In the model considered, there are two sensors: a peripheral sensor and a coordinating sensor. At each time, the peripheral sensor decides whether to stop and send an alarm to the coordinating sensor or to continue making observations. Once the coordinating sensor receives an...
In some recent applications involving large-scale data analytics, a plurality of data streams are sequentially observed in parallel, and the statistical decision maker is asked to screen out among these data streams those that exhibit certain characteristics. Motivated by such setting, in this work, a parallel sequential change detection model is investigated. In the model, a plurality of independent...
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