Pinball loss minimization for one-bit compressive sensing: Convex models and algorithms
نویسندگان
چکیده
منابع مشابه
Pinball Loss Minimization for One-bit Compressive Sensing
The one-bit quantization can be implemented by one single comparator, which operates at low power and a high rate. Hence one-bit compressive sensing (1bit-CS) becomes very attractive in signal processing. When the measurements are corrupted by noise during signal acquisition and transmission, 1bit-CS is usually modeled as minimizing a loss function with a sparsity constraint. The existing loss ...
متن کاملSupplementary Material: Efficient Algorithms for Robust One-bit Compressive Sensing
We consider the following general optimization problem min x2≤1 −x ⊤ y + γx 1. (15) Before we proceed, we need the following lemma. Lemma 6. The solution to the optimization problem min x 1 2 (x − y) 2 + γ|x| is given by P γ (y) = 0, if |y| ≤ γ; sign(y)(|y| − γ), otherwise. where P γ (·) is the soft-thresholding operator defined in (7) (Donoho, 1995).
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While the conventional compressive sensing assumes measurements of infinite precision, onebit compressive sensing considers an extreme setting where each measurement is quantized to just a single bit. In this paper, we study the vector recovery problem from noisy one-bit measurements, and develop two novel algorithms with formal theoretical guarantees. First, we propose a passive algorithm, whi...
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One-bit measurements widely exist in the real world and can be used to recover sparse signals. This task is known as one-bit compressive sensing (1bit-CS). In this paper, we propose novel algorithms based on both convex and nonconvex sparsity-inducing penalties for robust 1bit-CS. We consider the dual problem, which has only one variable and provides a sufficient condition to verify whether a s...
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The problem of 1-bit compressive sampling is addressed in this paper. We introduce an optimization model for reconstruction of sparse signals from 1-bit measurements. The model targets a solution that has the least 0-norm among all signals satisfying consistency constraints stemming from the 1-bit measurements. An algorithm for solving the model is developed. Convergence analysis of the algorit...
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ژورنال
عنوان ژورنال: Neurocomputing
سال: 2018
ISSN: 0925-2312
DOI: 10.1016/j.neucom.2018.06.070