RIRIS - Room Impulse Response Interpolation with Shearlets

1. INTRODUCTION

RIRIS (Room Impulse Response Interpolation with Shearlets) contains the MATLAB implementation of RIR interpolation using fast shearlet transforms¹², validated with experimental data in three rooms measured at KTH Royal Institute of Technology.

RIRIS is covered by a GPL v3 license (see LICENSE for license terms).

2. INSTALLATION

Download the .zip file and extract it in your folder of preference. There is no need to install files, as the dependencies are added (and removed) automatically when running the main script.

OBS! The folder dependencies must be in the same directory as the main script. The computer storage required by RIRIS is 170 MB.

2. MAIN SCRIPT

2.1. RIRIS

Run this script to perform the iterative thresholding of shearlet coefficients in a room of choice (Munin,Freja,Balder), with specific no. decomposition scales and no. iterations.

The optimal threshold parameter is read from dependencies/regularizationData so as to decrease the running times of the whole script. If the user wishes to compute the Pareto curves and estimate the optimal threshold anyway, then the binary variable paretoFlag in Line97 should be set to 1. OBS: This may incur overall longer computation times of RIRIS.

Once the interpolation is finished, Figure 1 outputs the results in the form of RIR images (under-sampled, interpolated, and reference), and Figure 2 outputs the modal assurance criterion ($\textrm{MAC}$) vs. frequency. In addition, the normalized mean-squared error ($\textrm{NMSE}$), as well as the computation time ($\textrm{CT}$), are displayed in the Command Window.

Example of usage: interpolate RIRs in lecture room Balder, provided an under-sampling ratio of 3, a shearlet dictionary with 4 scales, and running 15 thresholding (ISTA ³) iterations:

RIRIS('Balder',3,4,15);

This is how the interpolation results look like:

OBS! A fifth input argument, saveFlag, is accepted by RIRIS, which, if set to TRUE, stores the results (NMSE, MAC, image, image_recov,…) into a .mat file in the folder dependencies/results.

3. DEPENDENCIES

3.1. BASIS FUNCTIONS

Cone-adapted shearlets for every room (i.e., every $(T,M)$ combination) and for values of $\tau$ (decomposition scales) $2, 3, 4$, and $5$. These are in the form of look-up tables.

Example: ‘Balder_tau_4.mat’ contains the $K \times T \times M$ shearlet bases used in the meeting room Balder provided a 4-scale dictionary (i.e. $K = 61$).

These basis functions are computed with the Fast Finite Shearlet Transform toolbox, copyright 2014 Sören Häuser.

OBS! In order to run the code with arbitrarily-sized RIR images, shearlet systems must be created with the desired image dimensions. You can do this in Matlab using cone-adapted bandlimited shearlet systems.

3.2. MEASUREMENT DATA

Reference RIR images for each room. These .mat files are loaded with the utility function loadRIRs. The content of each file is a structure out with fields:

• image: $T \times M$ numeric array
• fs: temporal sampling frequency
• T: no. time samples
• M: no. microphones

3.3. REGULARIZATION DATA

Optimal threshold parameters $\beta^\star$, for every room and no. decomposition scales, at which $J(\beta)$ attains a maximum (trade-off sparsity and model misfit).

Example: ‘Freja_u3_tau3.mat’ contains the value of $\beta^\star$ in Freja, given an under-sampling ratio of 3, and 3 decomposition scales.

In the main script, the default is to load these parameters (avoiding the need to maximize the curvature every time). If one wants to run the maximization of $J(\beta)$ anyway, setting ‘paretoFlag’ to 1 in Line 89 does the trick. Be careful on where these end up stored.

The content of each .mat file is a structure reguThresh with fields:

• beta_star: value of $\beta$ at which $J(\beta)$ attains a maximum
• Jcurve: curvature function $J(\beta)$
• beta_set: pool of values of $\beta$ for maximization of $J(\beta)$

3.4. UTILITY FUNCTIONS

Below is an overview of the utility functions that are used in the main script. More detailed explanations can be found in their individual preambles.

3.4.1. computePareto: compute L-curve corner with cubic spline interpolation

3.4.2. expansionMtrx: generate expansion matrix restricting vertical-like shearlets

3.4.3. extRIRimage: perform spatial extrapolation of RIR image

3.4.4. ffst: vectorized fast finite shearlet transform (both in/out are vectors)

3.4.5. hline: function to plot horizontal line on an axis

3.4.6. iffst: same as 3.4.4. but inverse transform

3.4.7. ista: iterative soft thresholding algorithm

3.4.8. loadRIRs: load RIR reference image

3.4.9. lpbp1D: 1D linear predictive border padding of spatial dimensions

3.4.10. perforMetrics: assessment function that outputs performance metrics and figures

3.4.11. selectionMtrx: generate masking (selection) matrix

3.4.12. vline: function to plot vertical line on an axis

4. RELEASE HISTORY

Release #1	 RIRIS v1.0 	E. Zea	2023-04-27

5. FEEDBACK & CONTACT INFORMATION

Your questions, suggestions, and feedback can help improve the quality of this software. Feel free to contact me at

Elias Zea (zea@kth.se)
Marcus Wallenberg Laboratory for Sound and Vibration Research
Department of Engineering Mechanics
KTH Royal Institute of Technology
Teknikringen 8
10044 Stockholm, SWEDEN

6. LEGAL INFORMATION

Copyright 2019 Elias Zea

This software was written by Elias Zea, and it was created during a postdoctoral period at the Marcus Wallenberg Laboratory for Sound and Vibration Research, KTH Royal Institute of Technology.

RIRIS is free software. You can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 3 of the License, or (at your option) any later version. If not stated otherwise, this applies to all files contained in this package and its sub-directories.

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with this program; if not, write to the Free Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA

Footnotes

1. E. Zea, “Compressed sensing of impulse responses in rooms of unknown properties and contents,” J. Sound Vib. 459, 114871 (2019). ↩

2. S. Häuser, G. Steidl, “Fast finite shearlet transform: a tutorial,” ArXiv 1202.1773, 1-41 (2012). ↩

3. I. Daubechies, M. Defrise, C. De Mol, “An iterative thresholding algorithm for linear inverse problems with a sparsity constraint,” Comm. Pure Appl. Math. 57, 1413-1457 (2004). ↩