Autocalibrated signal reconstruction from linear measurements using adaptive GAMP

Kamilov, Ulugbek S.; Bourquard, Aurélien; Bostan, Emrah; Unser, Michaël

doi:10.1109/icassp.2013.6638801

Cited by 8 publications

(6 citation statements)

References 15 publications

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“…One work on blind calibration that used a GAMP-based algorithm is [21], where the authors combine GAMP with expectation maximization-like learning. That paper, however, considers a setting different from ours in the sense that the unknown gains are on the signal components not on the measurement components.…”

Section: Relation To Gamp and Some Of Its Existing Extensionsmentioning

confidence: 99%

Blind sensor calibration using approximate message passing

2015

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The ubiquity of approximately sparse data has led a variety of communities to great interest in compressed sensing algorithms. Although these are very successful and well understood for linear measurements with additive noise, applying them on real data can be problematic if imperfect sensing devices introduce deviations from this ideal signal acquisition process, caused by sensor decalibration or failure. We propose a message passing algorithm called calibration approximate message passing (Cal-AMP) that can treat a variety of such sensor-induced imperfections. In addition to deriving the general form of the algorithm, we numerically investigate two particular settings. In the first, a fraction of the sensors is faulty, giving readings unrelated to the signal. In the second, sensors are decalibrated and each one introduces a different multiplicative gain to the measurements. Cal-AMP shares the scalability of approximate message passing, allowing to treat big sized instances of these problems, and experimentally exhibits a phase transition between domains of success and failure.

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Section: Relation To Gamp and Some Of Its Existing Extensionsmentioning

confidence: 99%

Blind sensor calibration using approximate message passing

2015

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“…MMV CS with input gain uncertainty, i.e., recovering possibly-sparse C from a noisy observation of Z = A Diag(b)C, where A is known and b is unknown, was considered in [34]. There, G-AMP estimation of C was alternated with EM estimation of b using the EM-AMP framework from [26].…”

Section: Relation To Previous Workmentioning

confidence: 99%

“…There, G-AMP estimation of C was alternated with EM estimation of b using the EM-AMP framework from [26]. As such, [34] does not support a prior on b.…”

Section: Relation To Previous Workmentioning

confidence: 99%

Parametric Bilinear Generalized Approximate Message Passing

Parker

Schniter

2016

IEEE J. Sel. Top. Signal Process.

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“…. , L are correlated, hence we can extend the same approach using quadratic measurements as in (10), but without discarding the phase information in the measurements that can now be relevant for reconstruction. Let us define the cross measurements, g i,k,ℓ as…”

Section: Phase Calibrationmentioning

confidence: 99%

“…Perturbations in a parameterized measurement matrix have been estimated along with the signal in [9]. Calibration for unknown scaling of the input signal using the generalized approximate message passing (GAMP) algorithm has been considered in [10]. The scenario of calibration for the unknown gains introduced by the sensors has been investigated in [11], also using GAMP.…”

Section: Introductionmentioning

confidence: 99%

Convex Optimization Approaches for Blind Sensor Calibration Using Sparsity

Bilen

Puy

Gribonval

et al. 2014

IEEE Trans. Signal Process.

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Abstract-We investigate a compressive sensing framework in which the sensors introduce a distortion to the measurements in the form of unknown gains. We focus on blind calibration, using measures performed on multiple unknown (but sparse) signals and formulate the joint recovery of the gains and the sparse signals as a convex optimization problem. We divide this problem in 3 subproblems with different conditions on the gains, specifially (i) gains with different amplitude and the same phase, (ii) gains with the same amplitude and different phase and (iii) gains with different amplitude and phase. In order to solve the first case, we propose an extension to the basis pursuit optimization which can estimate the unknown gains along with the unknown sparse signals. For the second case, we formulate a quadratic approach that eliminates the unknown phase shifts and retrieves the unknown sparse signals. An alternative form of this approach is also formulated to reduce complexity and memory requirements and provide scalability with respect to the number of input signals. Finally for the third case, we propose a formulation that combines the earlier two approaches to solve the problem. The performance of the proposed algorithms is investigated extensively through numerical simulations, which demonstrates that simultaneous signal recovery and calibration is possible with convex methods when sufficiently many (unknown, but sparse) calibrating signals are provided.

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Autocalibrated signal reconstruction from linear measurements using adaptive GAMP

Cited by 8 publications

References 15 publications

Blind sensor calibration using approximate message passing

Blind sensor calibration using approximate message passing

Parametric Bilinear Generalized Approximate Message Passing

Convex Optimization Approaches for Blind Sensor Calibration Using Sparsity

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