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.
翻译:鉴于脉冲图像源分布稀少所产生的声场,这些源的连续 3D 位置和振幅能否从一组有限地点的离散、带宽测量中恢复,例如多声室冲动反应?借用超分辨率成像的最新进展,可以证明,这一非线性、非阴道反向问题可以有效地放松为R3. 这里引入的线性操作员来自与接收器反应相结合的自由场无热波方程式的基本解决方案。建议对滑动的弗兰克-沃夫算法进行修改,以便从数字上解决离电网(即连续的3D空间)的问题。模拟实验表明,在随机矩形室内,利用任意放置的紧凑的32个频道球状麦克风阵列,可以实现近速恢复数百个图像源。还研究了噪音、取样率和阵列直径对结果的影响。