3 research outputs found
Vector Approximate Message Passing Algorithm for Structured Perturbed Sensing Matrix
In this paper, we consider a general form of noisy compressive sensing (CS)
where the sensing matrix is not precisely known. Such cases exist when there
are imperfections or unknown calibration parameters during the measurement
process. Particularly, the sensing matrix may have some structure, which makes
the perturbation follow a fixed pattern. While previous work has focused on
extending the approximate message passing (AMP) and LASSO algorithm to deal
with the independent and identically distributed (i.i.d.) perturbation, we
propose the robust variant vector approximate message passing (VAMP) algorithm
with the perturbation being structured, based on the recent VAMP algorithm. The
performance of the robust version of VAMP is demonstrated numerically.Comment: 6 pages, 3 figure
Asymptotically Optimal One-Bit Quantizer Design for Weak-signal Detection in Generalized Gaussian Noise and Lossy Binary Communication Channel
In this paper, quantizer design for weak-signal detection under arbitrary
binary channel in generalized Gaussian noise is studied. Since the performances
of the generalized likelihood ratio test (GLRT) and Rao test are asymptotically
characterized by the noncentral chi-squared probability density function (PDF),
the threshold design problem can be formulated as a noncentrality parameter
maximization problem. The theoretical property of the noncentrality parameter
with respect to the threshold is investigated, and the optimal threshold is
shown to be found in polynomial time with appropriate numerical algorithm and
proper initializations. In certain cases, the optimal threshold is proved to be
zero. Finally, numerical experiments are conducted to substantiate the
theoretical analysis
Robust Least Squares for Quantized Data Matrices
In this paper we formulate and solve a robust least squares problem for a
system of linear equations subject to quantization error in the data matrix.
Ordinary least squares fails to consider uncertainty in the operator, modeling
all noise in the observed signal. Total least squares accounts for uncertainty
in the data matrix, but necessarily increases the condition number of the
operator compared to ordinary least squares. Tikhonov regularization or ridge
regression is frequently employed to combat ill-conditioning, but requires
parameter tuning which presents a host of challenges and places strong
assumptions on parameter prior distributions. The proposed method also requires
selection of a parameter, but it can be chosen in a natural way, e.g., a matrix
rounded to the 4th digit uses an uncertainty bounding parameter of 0.5e-4. We
show here that our robust method is theoretically appropriate, tractable, and
performs favorably against ordinary and total least squares.Comment: 10 pages, 5 figure