期刊
IEEE TRANSACTIONS ON SIGNAL PROCESSING
卷 67, 期 21, 页码 5659-5670出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TSP.2019.2941070
关键词
Quantization (signal); Encoding; Machine learning; Dictionaries; Cost function; Signal processing algorithms; Distortion measurement; Sparse coding; dictionary learning; nonlinear measurements; saturation; quantization; 1-bit sensing
资金
- European Union [642685 MacSeNet]
Sparse coding and dictionary learning are popular techniques for linear inverse problems such as denoising or inpainting. However in many cases, the measurement process is nonlinear, for example for clipped, quantized or 1-bit measurements. These problems have often been addressed by solving constrained sparse coding problems, which can be difficult to solve, and assuming that the sparsifying dictionary is known and fixed. Here we propose a simple and unified framework to deal with nonlinear measurements. We propose a cost function that minimizes the distance to a convex feasibility set, which models our knowledge about the nonlinear measurement. This provides an unconstrained, convex, and differentiable cost function that is simple to optimize, and generalizes the linear least squares cost commonly used in sparse coding. We then propose proximal based sparse coding and dictionary learning algorithms, that are able to learn directly from nonlinearly corrupted signals. We show how the proposed framework and algorithms can be applied to clipped, quantized and 1-bit data.
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