Microphone arrays have long been used as a means of obtaining high quality sound capture. In general, the source signal is captured by multiple microphones and jointly processed to generate an enhanced output signal. For example, one or more microphones may be amplified while others are attenuated, resulting in a highly directional signal.
Current microphone array processing pipelines comprise two main stages, namely a linear beamformer that spatially filters the sound field, suppressing noise that comes from unwanted directions and a post-filter that performs additional noise reduction on the beamformer output signal. The output of the linear beamformer stage has some degree of noise reduction and generally improves perceptual quality. The output of the post-filter stage typically has much better noise reduction, but introduces artifacts into the output signal, which degrades the perceptual quality. As a result, in scenarios like videoconferencing and VoIP, the users/system designers are stuck with a choice of either minimal distortions but not much noise reduction or more noise reduction but significant distortions and artifacts.
This Summary is provided to introduce a selection of representative concepts in a simplified form that are further described below in the Detailed Description. This Summary is not intended to identify key features or essential features of the claimed subject matter, nor is it intended to be used in any way that would limit the scope of the claimed subject matter.
Briefly, various aspects of the subject matter described herein are directed towards a technology by which an adaptive beamformer is used to process input signals from microphones based on an estimated signal received from a pre-filter. In one aspect, the adaptive beamformer computes its parameters (e.g., weights) based on the estimate via a log-magnitude-domain objective function.
In one aspect, the pre-filter may include a time invariant beamformer and/or a non-linear spatial filter. In an alternative aspect, the pre-filter may include a spectral filter.
In one aspect, the computed parameters may be adjusted based on a constraint. The constraint may be selectively applied only at desired times.
Other advantages may become apparent from the following detailed description when taken in conjunction with the drawings.
The present invention is illustrated by way of example and not limited in the accompanying figures in which like reference numerals indicate similar elements and in which:
Various aspects of the technology described herein are generally directed towards a sound processing system that achieves both significant noise reduction and improved perceptual quality. In general, the approach works by reversing the order of the two processing blocks. First, as represented in
Further, performing the processing in this manner benefits from a new objective function for the array. This objective function, called Log Minimum Mean Squared Error, results in significant noise reductions and significant improvements in perceptual quality over other techniques.
Thus, as represented in
By way of example of more particular components, for frames of signals to process,
Instead of using this signal as the output, it is further processed and sent to an adaptive beamformer 206. More particularly, the phase may be discarded and the magnitude kept. The adaptive beamformer uses this magnitude estimate, which is a function of time, to dynamically compute parameters for varying the input signals from the microphones.
To this end, an error function may be minimized, e.g., errort=(|Dt|−|Yt|)2, that is, the adaptive beamformer 206 may use a magnitude-domain objective function, e.g., magnitude-minimum mean squared error (Mag-MMSE).
Alternatively, the adaptive beamformer 206 may use a Log-domain (Log-MMSE) objective function: errort=(log|Dt|−log|Yt|)2, or errortt2=(log|Dt|2−log|Yt|2)2. This takes advantage of the knowledge that a log operation is similar to the compression that occurs in the human auditory system and as a result, log-domain optimization is believed to be more perceptually relevant than spectral optimization. Secondly, because of the compressive nature of the log operation at large values, large differences in magnitude produce relatively small differences in the log domain. As a result, the log domain optimization is robust to errors in the estimation of the target signal's magnitude.
Also shown in
Turning to beamformer technology in general, assume that a source signal Dt(ω) is captured by the array 102 of M microphones. The received signals Xt(ω)={X1,t(ω), . . . , XM,t(ω)} are then segmented into a sequence of overlapping frames, converted to the frequency domain using a short-time Fourier transform (STFT) and processed by a set of beamformer parameters Wt(ω)={W1,t(ω), . . . , WM,t(ω)} to create an output signal Yt(ω) as follows:
If a time-invariant beamformer is being employed, the weights do not vary over time, i.e., Wt(ω)=W(ω). Note that as described herein, the various frequency bins may be processed independently, and as such are not referred to (frequency bin ω) for simplicity.
In an adaptive beamformer the beamformer parameters (e.g., weights) Wt are learned in an online manner, as samples are received. Most adaptive beamformers examine the derivation of time-invariant beamformers and substitute instantaneous estimates for long-term statistics. For example, the well-known Frost beamformer (based upon a Minimum Variance Distortionless Response or MVDR technology) minimizes the power of the array's output signal, subject to a linear constraint that specifies zero distortion in gain or phase from the desired look direction. This results in the following objective function:
where C describes the steering vector in the desired look direction θ and F defines the desired frequency response in this direction. To derive an online adaptive version of an MVDR beamformer, one known solution used a gradient descent method whereby the weights at a given time instant are a function of the previous weights and the gradient of the objective function with respect to these weights.
W
t+1
=W
t−μ∇WH(Wt) (3)
These updated weights need to satisfy the distortionless constraint, such that
W
t+1
H
C=F (4)
By taking the derivative of H(W), substituting (3) into (4), and solving for Wt+1, it can be shown that the adaptive beamformer has the following update equation:
W
t+1
=P(Wt−μYtHXt)+F (5)
where μ is the learning rate, P=(I−C(CHC)−1CH) and F=C(CHC)C(CHC)−1F
Nonlinear spatial filtering is conventionally used as a post-filtering algorithm to achieve further noise reduction of the output channel of a time-invariant beamformer. To this end, in a given frame and frequency bin, an Instantaneous DOA (IDOA) vector Δt is formed from the phase differences between the microphone signals in non-repetitive pairs. The spatial filter is formed by computing a probability that an observed Δt originated from the desired look direction θ. This is done by first computing the Euclidean distance between Δt and Δθ, which is the IDOA vector generated by an ideal source originating from θ. This distance in IDOA space is then converted to a distance in physical space, denoted Γtθ. For a linear array, this physical distance represents the absolute difference in radians between the angle of arrival of Xt and the desired look direction θ.
In the absence of noise, the distance Γtθ is equal to zero if Δt=Δθ. To reflect the presence of noise, it is assumed that Γtθ follows a Gaussian distribution with zero mean and variance σθ2, i.e., p(Γtθ)˜N(0, σθ2). Estimates of the variance σθ2 are made online during non-speech segments for a discrete set of look directions.
The nonlinear spatial filter is computed as the ratio of the probabilities of Γtθt and Γmaxθ, defined as the distance that generates the highest probability for the given look direction. This can be written as:
Note that is a real-valued function between 0 and 1. Thus, the filter, applied to the array output signal, controls the gain only. Because the phase is not compensated, this time-varying filter shares the same properties as other gain-based noise suppression algorithms, e.g., it can significantly increase the output SNR, but also cause significant distortion and artifacts.
In one implementation, the adaptive beamformer described herein is a log-MMSE adaptive beamformer. The adaptive beamformer described herein assumes no prior knowledge of the desired source signal Dt. However, as represented in
In one implementation, the beamformer may comprise a minimum mean squared error beamformer in the log domain. Note that operating in the log domain rather than in the magnitude or power spectral domains has advantages related to perceptual relevance and robustness to errors in estimated spectral magnitudes. A suitable error function is thus mean squared error of the log spectra of the desired signal and the array output:
Since online adaptation is performed, the expectation with the instantaneous error is:
Taking the derivative of (8) with respect to the filter parameters gives:
To avoid changing the weights too abruptly between frames, a frame's weights may be smoothed with a prior frame's weights, with a value μ (which may be fixed or dynamically adjustable) used as a balancing factor, that is, using (9), the gradient descent update rule can be written as:
The update equation (11) defines an unconstrained adaptive beamformer. If there are reliable estimates of the desired signal, this may be sufficient. However, if the desired signal approaches zero, an unconstrained adaptive beamformer may approach the degenerate solution Wt=0. Therefore, it may be desirable to impose a constraint on the adaptation.
To this end, there is described linearly constrained Log-MMSE beamforming. Consider that the adaptive beamformer is operating with a desired look direction that specifies C and a desired array response in that direction that specifies F. Thus, in this case, the objective function becomes:
Taking the gradient of (12) produces the following gradient expression:
This produces the following constrained update expression:
which needs to satisfy the linear constraint:
C
H
W
t+1
=F (15)
where a real-valued function for is assumed for F so that CHW=WHC. The value of λ can be found by substituting (14) into (15). Then, by substituting this value back into (14) and rearranging terms, the update expression is:
where P and F are defined above.
During processing, there may be times that is may be desirable to have the constraint active or inactive. For example, in long periods of silence, running the beamformer in a constrained mode is advantageous to prevent the filter weights from degenerating to the zero solution, while during periods of desired signal activity, it is desirable to have the beamformer best match the estimated log spectrum of the desired signal, irrespective of any constraints. Equations (11) and (16) show that these two modes of operation can be combined into a single update equation given by:
Turning to another aspect, because the system operates on log spectral values, finding an optimal value of Wt requires a nonlinear iterative optimization method. However, because of the nonlinearity between the log spectral observations and the linear beamformer weights, the objective function is no longer quadratic. As a result, methods for improving the convergence of LMS algorithms, e.g. Normalized LMS (NLMS), cannot be applied. In order to improve convergence, a known nonlinear NLMS algorithm is used, in which the step size is normalized by the norm of the gradient of the output signal, log(|Y|2), with respect to the parameters being optimized, W. This results in the following normalized step size expression:
where 0<{tilde over (μ)}<1.
The invention is operational with numerous other general purpose or special purpose computing system environments or configurations. Examples of well known computing systems, environments, and/or configurations that may be suitable for use with the invention include, but are not limited to: personal computers, server computers, hand-held or laptop devices, tablet devices, multiprocessor systems, microprocessor-based systems, set top boxes, programmable consumer electronics, network PCs, minicomputers, mainframe computers, distributed computing environments that include any of the above systems or devices, and the like.
The invention may be described in the general context of computer-executable instructions, such as program modules, being executed by a computer. Generally, program modules include routines, programs, objects, components, data structures, and so forth, which perform particular tasks or implement particular abstract data types. The invention may also be practiced in distributed computing environments where tasks are performed by remote processing devices that are linked through a communications network. In a distributed computing environment, program modules may be located in local and/or remote computer storage media including memory storage devices.
With reference to
The computer 310 typically includes a variety of computer-readable media. Computer-readable media can be any available media that can be accessed by the computer 310 and includes both volatile and nonvolatile media, and removable and non-removable media. By way of example, and not limitation, computer-readable media may comprise computer storage media and communication media. Computer storage media includes volatile and nonvolatile, removable and non-removable media implemented in any method or technology for storage of information such as computer-readable instructions, data structures, program modules or other data. Computer storage media includes, but is not limited to, RAM, ROM, EEPROM, flash memory or other memory technology, CD-ROM, digital versatile disks (DVD) or other optical disk storage, magnetic cassettes, magnetic tape, magnetic disk storage or other magnetic storage devices, or any other medium which can be used to store the desired information and which can accessed by the computer 310. Communication media typically embodies computer-readable instructions, data structures, program modules or other data in a modulated data signal such as a carrier wave or other transport mechanism and includes any information delivery media. The term “modulated data signal” means a signal that has one or more of its characteristics set or changed in such a manner as to encode information in the signal. By way of example, and not limitation, communication media includes wired media such as a wired network or direct-wired connection, and wireless media such as acoustic, RF, infrared and other wireless media. Combinations of the any of the above may also be included within the scope of computer-readable media.
The system memory 330 includes computer storage media in the form of volatile and/or nonvolatile memory such as read only memory (ROM) 331 and random access memory (RAM) 332. A basic input/output system 333 (BIOS), containing the basic routines that help to transfer information between elements within computer 310, such as during start-up, is typically stored in ROM 331. RAM 332 typically contains data and/or program modules that are immediately accessible to and/or presently being operated on by processing unit 320. By way of example, and not limitation,
The computer 310 may also include other removable/non-removable, volatile/nonvolatile computer storage media. By way of example only,
The drives and their associated computer storage media, described above and illustrated in
The computer 310 may operate in a networked environment using logical connections to one or more remote computers, such as a remote computer 380. The remote computer 380 may be a personal computer, a server, a router, a network PC, a peer device or other common network node, and typically includes many or all of the elements described above relative to the computer 310, although only a memory storage device 381 has been illustrated in
When used in a LAN networking environment, the computer 310 is connected to the LAN 371 through a network interface or adapter 370. When used in a WAN networking environment, the computer 310 typically includes a modem 372 or other means for establishing communications over the WAN 373, such as the Internet. The modem 372, which may be internal or external, may be connected to the system bus 321 via the user input interface 360 or other appropriate mechanism. A wireless networking component 374 such as comprising an interface and antenna may be coupled through a suitable device such as an access point or peer computer to a WAN or LAN. In a networked environment, program modules depicted relative to the computer 310, or portions thereof, may be stored in the remote memory storage device. By way of example, and not limitation,
An auxiliary subsystem 399 (e.g., for auxiliary display of content) may be connected via the user interface 360 to allow data such as program content, system status and event notifications to be provided to the user, even if the main portions of the computer system are in a low power state. The auxiliary subsystem 399 may be connected to the modem 372 and/or network interface 370 to allow communication between these systems while the main processing unit 320 is in a low power state.
While the invention is susceptible to various modifications and alternative constructions, certain illustrated embodiments thereof are shown in the drawings and have been described above in detail. It should be understood, however, that there is no intention to limit the invention to the specific forms disclosed, but on the contrary, the intention is to cover all modifications, alternative constructions, and equivalents failing within the spirit and scope of the invention.