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Compressed sensing with quantized measurements
, 2010
"... We consider the problem of estimating a sparse signal from a set of quantized, Gaussian noise corrupted measurements, where each measurement corresponds to an interval of values. We give two methods for (approximately) solving this problem, each based on minimizing a differentiable convex function p ..."
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Cited by 19 (0 self)
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We consider the problem of estimating a sparse signal from a set of quantized, Gaussian noise corrupted measurements, where each measurement corresponds to an interval of values. We give two methods for (approximately) solving this problem, each based on minimizing a differentiable convex function plus an regularization term. Using a first order method developed by Hale et al, we demonstrate the performance of the methods through numerical simulation. We find that, using these methods, compressed sensing can be carried out even when the quantization is very coarse, e.g., 1 or 2 bits per measurement.
Optimal Estimation of Deterioration from Diagnostic Image Sequence
 IEEE TRANSACTIONS ON SIGNAL PROCESSING, SUBMITTED MAY 2007
, 2007
"... This paper considers estimation of pixelwise monotonic increasing (or decreasing) data from a time series of noisy blurred images. The motivation comes from estimation of mechanical structure damage that accumulates irreversibly over time. We formulate a Maximum A posteriory Probablity (MAP) estima ..."
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Cited by 5 (4 self)
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This paper considers estimation of pixelwise monotonic increasing (or decreasing) data from a time series of noisy blurred images. The motivation comes from estimation of mechanical structure damage that accumulates irreversibly over time. We formulate a Maximum A posteriory Probablity (MAP) estimation problem and find a solution by direct numerical optimization of a loglikelihood index. Spatial continuity of the damage is modeled using a Markov Random Field (MRF). The MRF prior includes the temporal monotonicity constraints. We tune the MRF prior, using a spatial frequency domain loopshaping technique to achieve a tradeoff between noise rejection and signal restoration properties of the estimate. The MAP optimization is a largescale Quadratic Programming (QP) problem that could have more than a million of decision variables and constraints. We describe and implement an efficient interiorpoint method for solving such optimization problem. The method uses a preconditioned conjugate gradient method to compute the search step. The developed QP solver relies on the special structure of the problem and can solve the problems of this size in a few tens of minutes, on a PC. The application example in the paper describes structural damage images obtained using a Structural Health Monitoring (SHM) system. The damage signal is distorted by environmental temperature that varies for each acquired image in the series. The solution for the experimental data is demonstrated to provide an excellent estimate of the damage accumulation trend while rejecting the spatial and temporal noise.
Fast Decoding and Hardware Design for BinaryInput Compressive Sensing
"... Abstract—Binaryinput compressive sensing (BiCS) has recently been applied to wireless communicationsasamodulatedcoding scheme for seamless rate adaptation. Different from conventional channel codes which generate binary symbols with logicalOR (XOR) operations, BiCS generates multilevel symbols thr ..."
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Abstract—Binaryinput compressive sensing (BiCS) has recently been applied to wireless communicationsasamodulatedcoding scheme for seamless rate adaptation. Different from conventional channel codes which generate binary symbols with logicalOR (XOR) operations, BiCS generates multilevel symbols through weighted sum operation. Although BiCS can be decoded by message passing, it needs to compute the convolution of probability functions in each iteration. The high decoding complexity has prevented the technique from being applied to practical use. In this paper, we propose a fast BiCS decoding algorithm and its corresponding partialparallel hardware design. In this algorithm, we first build lookup tables to solve the computationally intensive problem of convolution. Through these tables, we successfully convert the convolution of probabilities into the polynomial of some exponential terms. This key step allows us to use loglikelihood ratio as message in message passing decoding and a fast algorithm is developed by approximate computing. We further design a partialparallel hardware decoder. To avoid memory collision, we propose a multilevel cyclicshift approach to generate the CS measurement matrix. We design horizontal unit processors with the proposed tables for iterative computing. Our analyses show that the proposed fast algorithm can reduce multiplications by nearly 90%. The decoding speed of our fieldprogrammable gate array design reaches the range of communication rate in modern wireless networks. Index Terms—Compressive sensing (CS), fast decoding, message passing, random projection codes, wireless rate adaptation.