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3D sound reconstruction is the application of reconstruction techniques to 3D sound localization technology. These methods of reconstructing 3D sound can be used to recreate sounds to match natural environments and provide spatial cues of the sound source. They also see applications in creating 3D visualizations on a sound field to include physical aspects of sound waves including direction, pressure, and intensity.

Motivation and Applications
When reconstructing recorded 3D audio and visualizing sound fields, sound localization and reconstructing the reverberation and sound pressure are critical to produce robust and natural-sounding audio. There are various techniques to process sound so that the spatial cues can be reproduced when reconstructing sound. This technology sees a demand in entertainment as audiences look for the ambience of a live performance reproduced through their speakers. Reconstructing a 3D sound field also becomes critical in military applications where visualizing pressure in a 3D sound field can help determine location of sound sources. Reconstructing sound fields is also applicable to medical imaging and measurement of points in ultrasound.

Problem Statement and Basic Concepts
Various methods of determining the location of a sound source have been determined through 3D sound localization which determines the location based off a variety of attributes and makes use of multiple microphone arrays, binaural hearing methods, and HRTF(Head-related transfer function). These methods are coupled with other signal processing techniques to measure the impulse response over lengths of time to determine the intensity components in different directions. Combining intensity of sound with direction, a 3D sound field can be determined and various physical qualities that create the resulting changes in intensity can be reconstructed. Reconstructing a 3D sound field takes into account the localization of the sound source as well as the physical aspects of the environment of the original signal source.

Listening room
When recreating sound there are two possible ways for a listener to perceive the sound, either through headphones or through loudspeakers. To properly introduce enough sound sources for a listener to experience 3D sound with directionality, a virtual room is created to be reproduced through headphones. With loudspeakers, the placement and number of loudspeakers determines whether the 3D sound is reconstructed with the correct amount of depth. A simple model that reconstructs the original sound consists of five speakers, placed in the formation: center, 30° to the left, 110° to the left, 30° to the right, and 110° to the right. This is the ITU-R recommended listening room, in which several 3D sound systems and reconstruction techniques are developed. To reconstruct sound in this speaker formation the localization technique of using HRTF(Head-related transfer function) and the sound source signal is performed. This convolution is panned to each of the loudspeakers depending on the direction and location. The energy of each signal for each speaker is determined by the selection of control points within the listening room.

Reverberation Reconstruction
The reverberation reconstruction is done by a four-point microphone setup to measure reverberations in the virtual reconstructed listening room. Each microphone measures an impulse response using a Time-Stretched Pulse(TSP) as the signal. The measured impulse response includes information for various time frames with various sound sources. The data obtained by measuring various sound sources at different time frames can be applied to the 5-speaker 3D sound system. The system with the reverberation reconstruction convolves the HRTF with the impulse response from the signal recorded by the microphones. From this convolution, the energy is adjusted per the original time frame of the sound signal. A delay is added to the sound to match the time frame of the impulse response. The convolution and delays are applied to all the sound source data taken and summed for the resulting signal. The resulting signal contains the reverberation in the reconstructed signal when for a better quality sound to be played to listeners.

This method has a disadvantage as measurements taken by the microphone setup are assumed to include only one sound, while real-life reverberations include various sounds with overlap. The advantage of this method is that the signal that is reconstructed improves the 3D sound localization, as the direction of the sound source can be more easily perceived by the listener. This technique also improving the naturalness and clarity of the reconstructed sound with respect to the original. A drawback of this method is that the assumption of a single sound source, coupled with adding all the different values does not improve listeners perception of the size of the room, the perception of distance is not improved.

Laser Projections
In regards to a sound field, sound waves cause changes in air density to reflect possible changes in sound pressure caused by intensity of the source. A visual reconstruction of the sound field can be reproduced through the usage of a signal processing technique called,Tomography. The reconstruction of the sound field through projections is an alternative method that does not need the usage of various microphones to determine separate impulse responses. Instead sound pressure is measured using a laser Doppler vibrometer and all values on the path of the laser can be measured. This saves the number of points needed with using a setup of multiple microphones to determine the sound field.

A sound field produces changes in the air pressure of the room or area of measurement. Air pressure changes can be observed through changes in the refractive index, changes which can be observed through a laser passing through the areas of altered air pressure. The laser Doppler vibrometer works by pointing a laser through the sound field against a reflective surface so that the laser is reflected and the returning beam can be observed. Taking the intensities from the laser, the reconstruction of the sound field can be calculated using the Tomographic_reconstruction techniques of signal processing. Then using the Convolution Back Projection(CBP) method, the sound field can be visualized.

Near-Field Acoustical Holography
Another approach using tomography includes the application of Near-Field Acoustical Holography(NAH). Using NAH, a 2D sound field can be reconstructed from the use of light and the refraction in the medium the sound field is measured. This 2D sound field is a cross section of the 3D sound field.Due to the parallel nature of the reconstructed sound field with any cross section of the 3D sound field, the calculated 2D sound field can be considered as a convolution between the reconstruction and the propagating function. From this relationship, the wave number of the medium can be estimated through analysis of the water temperature. From the reconstruction and the estimated wave number, a cross section of the 2D sound field can be calculated. Then comparing the newly constructed 2D sound field and the reconstruction, a much better representation of the wave number can be obtained. Multiple 2D sound fields can be calculated, and given that they are cross sections of the 3D sound field, the 3D sound field can be reconstructed as well through this method.

This method is applicable primarily to ultrasound and the NAH method is readily applied to lower sound pressures. The experiment to determine this method is performed in water and can see various applications in medical imaging. The method works under the assumption that the wave number of the medium is constant. If the wave number is changing throughout the medium, the NAH method cannot reconstruct the 3D sound field as accurately.