论文标题
从房间脉冲响应中恢复图像源的3D恢复
Gridless 3D Recovery of Image Sources from Room Impulse Responses
论文作者
论文摘要
考虑到由脉冲图像源的稀疏分布产生的声场，这些来源的连续3D位置和振幅是否可以从离散的，偶然的磁场测量值中恢复，例如，在有限的位置，例如，多冰川室脉冲响应？从最新的超分辨率成像中借用，这表明这种非线性，非凸起逆问题可以在R3中的radon测量空间中有效地放松成凸线性逆问题。这里引入的线性操作员源于自由场非构态波方程与接收器的响应的基本解决方案。提出了滑动的Frank-Wolfe算法的改编，以数字地解决问题，即在连续的3D空间中解决问题。模拟实验表明，该方法使用任意放置的紧凑型32通道球形麦克风阵列在随机矩形房间中接近恢复了数百个图像源。还检查了噪声，采样率和阵列直径对这些结果的影响。
Given a sound field generated by a sparse distribution of impulse image sources, can the continuous 3D positions and amplitudes of these sources be recovered from discrete, bandlimited measurements of the field at a finite set of locations, e.g., a multichannel room impulse response? Borrowing from recent advances in super-resolution imaging, it is shown that this nonlinear, non-convex inverse problem can be efficiently relaxed into a convex linear inverse problem over the space of Radon measures in R3. The linear operator introduced here stems from the fundamental solution of the free-field inhomogenous wave equation combined with the receivers' responses. An adaptation of the Sliding Frank-Wolfe algorithm is proposed to numerically solve the problem off-the-grid, i.e., in continuous 3D space. Simulated experiments show that the approach achieves near-exact recovery of hundreds of image sources using an arbitrarily placed compact 32-channel spherical microphone array in random rectangular rooms. The impact of noise, sampling rate and array diameter on these results is also examined.
