论文标题
来自离散傅立叶变换的量化噪声样本的信号重建
Signal Reconstruction from Quantized Noisy Samples of the Discrete Fourier Transform
论文作者
论文摘要
在本文中，我们介绍了一种从一位或两位噪声观察的信号重建算法的两种变体（DFT）。 DFT的一位观察结果对应于其真实部分的符号，而DFT的两位观测值对应于DFT的真实部分和虚构部分的符号。我们专注于分析和模拟的图像，因此使用2D-DFT的符号。此类信号类别的这种选择受到此问题的先前工作的启发。对于我们的算法，我们表明信号重建中的预期平方平方误差（MSE）与采样率的倒数成正比。样品受已知分布的添加零均值噪声的影响。我们通过设计基于Banach固定点定理的收缩映射的算法来解决此信号估计问题。提供了具有四个基准图像的数值测试，以显示我们算法的有效性。用于图像重建质量评估的各种指标，例如PSNR，SSIM，ESSIM和MS-SSIM。在所有四个基准图像上，我们的算法在所有这些指标中都超过了最先进的图像。
In this paper, we present two variations of an algorithm for signal reconstruction from one-bit or two-bit noisy observations of the discrete Fourier transform (DFT). The one-bit observations of the DFT correspond to the sign of its real part, whereas, the two-bit observations of the DFT correspond to the signs of both the real and imaginary parts of the DFT. We focus on images for analysis and simulations, thus using the sign of the 2D-DFT. This choice of the class of signals is inspired by previous works on this problem. For our algorithm, we show that the expected mean squared error (MSE) in signal reconstruction is asymptotically proportional to the inverse of the sampling rate. The samples are affected by additive zero-mean noise of known distribution. We solve this signal estimation problem by designing an algorithm that uses contraction mapping, based on the Banach fixed point theorem. Numerical tests with four benchmark images are provided to show the effectiveness of our algorithm. Various metrics for image reconstruction quality assessment such as PSNR, SSIM, ESSIM, and MS-SSIM are employed. On all four benchmark images, our algorithm outperforms the state-of-the-art in all of these metrics by a significant margin.
