Patent Publication Number: US-11393488-B2

Title: Systems and methods for enhancing audio signals

Description:
CROSS REFERENCE TO RELATED APPLICATION 
     The present application is based on and claims the benefits of priority to Chinese Application No. 201910344914.2, filed Apr. 26, 2019, the entire content of which is incorporated herein by reference. 
     TECHNICAL FIELD 
     The present disclosure relates to systems and methods for audio signal processing, and more particularly to, systems and methods for enhancing an audio signal by reconfiguring audio signals separated from the audio signal. 
     BACKGROUND 
     Speech recognition technologies have been applied to many areas recently. Compared to the earlier applications for speech recognition such as automated telephone systems and medical dictation software, recent applications of speech recognition changed the way people interact with their devices, homes, and cars. 
     To obtain a satisfied speech recognition result, it is essential to have a high-quality audio signal as an input of a speech recognition system. However, in real-world, an acquired audio signal is usually a mixture of signals from multiple audio sources. For example, a speech recognition system may receive a mixed audio signal including a human speech and environmental noises. The speech signal can come from a point audio source and the noises can come from diffuse sound sources, e.g., natural sources such as echo, wind sound, waves, and other unnatural sound sources. In order to enhance the quality of the audio signal, separation of the speech signal from the noises is desirable. 
     BSS is a technique for separating specific sources from sound mixture without prior information, e.g., signal statistics, source location, etc. For example, independent component analysis (ICA) is one of the most commonly used BSS method. On the other hand, Nonnegative Matrix Factorization (NMF) is a popular dimension-reduction technique, employed for non-subtractive, part-based representation of non-negative data, i.e., speech magnitude or power spectrum. In particular, multi-channel nonnegative matrix factorization (MNMF) is developed to use the spatial covariance to model the mixing conditions of the recoding environment. Furthermore, post process is often deployed after multi-channels speech enhancement to further reduce the interference. Some conventional post processing methods includes the single-channel based methods and adaptive filter based methods. 
     However, while these conventional separation and post processing methods yield good performance in point source separation, they are often insufficient to suppress diffuse interferences. Techniques to enhance audio signals from diffuse sources need to be improved. Reducing diffuse noises in an audio signal and improving speech perceptual can greatly increase the accuracy of speech recognition results. 
     Embodiments of the disclosure address the above problems by methods and systems for enhancing audio signals. 
     SUMMARY 
     Embodiments of the disclosure provide a system for enhancing audio signals. The system may include a communication interface configured to receive multi-channel audio signals acquired from a common signal source. The system may further include at least one processor. The at least one processor may be configured to separate the multi-channel audio signals into a first audio signal and a second audio signal in a time domain. The at least one processor may be further configured to decompose the first audio signal and the second audio signal in a frequency domain to obtain a first decomposition data and a second decomposition data, respectively. The at least one processor may be also configured to estimate a noise component in the frequency domain based on the first decomposition data and the second decomposition data. The at least one processor may be additionally configured to enhance the first audio signal based on the estimated noise component. The system may also include a speaker configured to output the enhanced first audio signal. 
     Embodiments of the disclosure also provide a method for enhancing audio signals. The method may include receiving, by a communication interface, multi-channel audio signals acquired from a common signal source. The method may further include separating, by at least one processor, the multi-channel audio signals into a first audio signal and a second audio signal originated in a time domain. The method may also include decomposing, by the at least one processor, the first audio signal and the second audio signal in a frequency domain to obtain a first decomposition data and a second decomposition data, respectively. The method may additionally include estimating, by the at least one processor, a noise component in the frequency domain based on the first decomposition data and the second decomposition data. The method may also include enhancing, by the at least one processor, the first audio signal based on the estimated noise component. 
     Embodiments of the disclosure further provide a non-transitory computer-readable medium having instructions stored thereon that, when executed by one or more processors, causes the one or more processors to perform a method for enhancing audio signals. The method may include receiving multi-channel audio signals acquired from a common signal source. The method may further include separating the multi-channel audio signals into a first audio signal and a second audio signal originated in a time domain. The method may also include decomposing the first audio signal and the second audio signal in a frequency domain to obtain a first decomposition data and a second decomposition data, respectively. The method may additionally include estimating a noise component in the frequency domain based on the first decomposition data and the second decomposition data. The method may also include enhancing the first audio signal based on the estimated noise component. 
     It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the invention, as claimed. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1A  illustrates a block diagram of an exemplary system for reducing noise in an audio signal, according to embodiments of the disclosure. 
         FIG. 1B  illustrates a data flow diagram for reducing noise in an audio signal compatible with the embodiment of  FIG. 1A , according to embodiments of the disclosure. 
         FIG. 2  illustrates a flowchart of an exemplary method for reducing noise in an audio signal, according to embodiments of the disclosure. 
         FIG. 3  illustrates a flowchart of an exemplary method for decomposing a first audio signal and a second audio signal in a frequency domain, according to embodiments of the disclosure. 
         FIG. 4  illustrates a flowchart of an exemplary method for estimating a noise component of an audio signal in a frequency domain, according to embodiments of the disclosure. 
         FIG. 5  illustrates a flowchart of an exemplary method for enhancing an audio signal based on an estimated noise component, according to embodiments of the disclosure. 
     
    
    
     DETAILED DESCRIPTION 
     Reference will now be made in detail to the exemplary embodiments, examples of which are illustrated in the accompanying drawings. Wherever possible, the same reference numbers will be used throughout the drawings to refer to the same or like parts. 
     In some embodiments, an audio processing system and method is disclosed to reduce interference after multi-channel speech enhancement (MSE) algorithms, including but not limited to MNMF. For example, MNMF may be performed to separate the inputs into separated speech and interference channels. Speech and interference basis matrices are obtained from the corresponding channels. First, speech component is removed from interference bases, in order to prevent speech distortion. Then interference bases are used to reconstruct the MNMF separated speech spectra under multiplicative update (MU) rules, where only activation matrix is updated. Since interference bases exclude speech component, large distance between the reconstructed and the original speech spectra should exist in the region where speech energy is concentrated, like harmonics, or unvoiced speech. 
       FIG. 1A  illustrates a block diagram of an exemplary system for reducing noise in an audio signal, according to embodiments of the disclosure.  FIG. 1B  illustrates a data flow diagram for reducing noise in an audio signal compatible with the embodiment of  FIG. 1A , according to embodiments of the disclosure.  FIG. 1A  and  FIG. 1B  will be described together. 
     Consistent with the present disclosure, acquisition device  110  may acquire audio signals from audio source  101 . In some embodiments, audio source  101  may be a person who gives a speech in a noisy environment, a speaker that plays a speech, an audio book, a news broadcast, or a song in the noisy environment, etc. In some embodiments, acquisition device  110  may be a microphone device, a sound recorder, or the like. In some embodiments, acquisition device  110  may be a standalone audio receiving device or part of another device, such as a mobile phone, a wearable device, a headphone, a vehicle, a surveillance system, etc. 
     In some embodiments, acquisition device  110  may be configured to receive multi-channel signals, including, e.g., a first-channel signal  103  of a first channel and a second-channel signal  105  of a second channel. For example, acquisition device  110  may include two or more acquisition channels, or include two or more individual acquisition units. In some embodiments, audio signal of each channel includes a human speech and diffuse noises. Server  120  may receive the multi-channel audio signals from acquisition device  110 , and then reduce noises from the audio signal and enhance its quality. Server  120  may transform and decompose the two audio signals to obtain an enhanced speech signal based on an estimated noise component. 
     In some embodiments, as shown in  FIG. 1A , server  120  may include a communication interface  102 , a processor  104 , a memory  106 , and a storage  108 . In some embodiments, server  120  may have different modules in a single device, such as an integrated circuit (IC) chip (implemented as an application-specific integrated circuit (ASIC) or a field-programmable gate array (FPGA)), or separate devices with dedicated functions. In some embodiments, one or more components of server  120  may be located in a cloud, or may be alternatively in a single location or distributed locations. Components of server  120  may be in an integrated device, or distributed at different locations but communicate with each other through a network (not shown). 
     Communication interface  102  may send data to and receive data from components such as speaker  130  and acquisition device  110  via communication cables, a Wireless Local Area Network (WLAN), a Wide Area Network (WAN), wireless networks such as radio waves, a cellular network, and/or a local or short-range wireless network (e.g., Bluetooth™), or other communication methods. In some embodiments, communication interface  102  can be an integrated services digital network (ISDN) card, cable modem, satellite modem, or a modem to provide a data communication connection. As another example, communication interface  102  can be a local area network (LAN) card to provide a data communication connection to a compatible LAN. Wireless links can also be implemented by communication interface  102 . In such an implementation, communication interface  102  can send and receive electrical, electromagnetic or optical signals that carry digital data streams representing various types of information via a network. 
     Consistent with some embodiments, communication interface  102  may receive multi-channel audio data such as first-channel signal  103  and second-channel signal  105  of two channels acquired by acquisition device  110 . 
     Communication interface  102  may further provide the received data to storage  108  for storage or to processor  104  for processing. Communication interface  102  may also receive an enhanced audio signal generated by processor  104 , and provide the enhanced audio signal to a local speaker or any remote speaker (e.g., speaker  130 ) via a network. 
     Processor  104  may include any appropriate type of general-purpose or special-purpose microprocessor, digital signal processor, or microcontroller. Processor  104  may be configured as a separate processor module dedicated to enhancing audio signals. Alternatively, processor  104  may be configured as a shared processor module for performing other functions unrelated to audio signal enhancement. 
     As shown in  FIG. 1A , processor  104  may include multiple modules, such as a signal separation unit  142 , an NMF decomposition unit  144 , a noise estimation unit  146 , and a speech signal enhancing unit  148 , and the like. These modules (and any corresponding sub-modules or sub-units) can be hardware units (e.g., portions of an integrated circuit) of processor  104  designed for use with other components or software units implemented by processor  104  through executing at least part of a program. The program may be stored on a computer-readable medium, and when executed by processor  104 , it may perform one or more functions. Although  FIG. 1A  shows units  142 - 148  all within one processor  104 , it is contemplated that these units may be distributed among multiple processors located near or remotely with each other. 
     Consistent with some embodiments, signal separation unit  142  may be configured to separate the multi-channel audio signals (e.g., first-channel signal  103  and second-channel signal  105 ) into a first audio signal and a second audio signal. In some embodiments, a blind source separation (BSS) method may be performed for separating the speech and interference channel signals. Blind source separation is a technique for separating specific sources from sound mixture without prior information, e.g., signal statistics, source location, etc. 
     In some embodiments, a multi-channel nonnegative matrix factorization (MNMF) algorithm is employed for the blind source separation. MNMF utilizes a spatial covariance to model a mixing condition of a recoding environment. Under an assumption of instantaneous mixing in the frequency domain, MNMF with rank-1 can be implemented for the separation tasks. For example, as shown in  FIG. 1B , signal separation unit  142  may implement MNMF rank-1 module  150  to separate the multi-channel input into a separated speech channel (an example of the first audio signal) and a separated interference channel (an example of the second audio signal). 
     By utilizing information between channels, MNMF clusters the decomposed bases into specific sources in a blind situation. In some embodiments, using the rank-1 MNMF algorithm, most speech component goes to the separated speech channel. However, there is no complete separation between speech and noise. In particular, rank-1 MNMF suppresses little interference in the separated speech channel and some speech component may leak into the separated interference channel. As a result, the speech channel signal may consist mainly of the speech signal but also include some noises, while the interference channel signal may consist largely of noises but include a small amount of speech signal. That is, in general, the speech signal ratio of the speech channel signal is higher than the speech signal ratio of the interference channel signal. Consistent with some embodiments, a first speech signal ratio of the speech channel signal is higher than a first threshold and a second speech signal ratio of the interference channel signal is lower than a second threshold, and the second threshold is smaller than the first threshold. It is contemplated that other blind source separation methods may also be used to separate the multi-channel audio signals to achieve the same or similar separation results. 
     In some embodiments, the remaining units of processor  104 , including NMF decomposition unit  144 , noise estimation unit  146  and signal enhancing unit  148 , may implement postprocessing module  160  of  FIG. 1B , which includes sub-modules  161 - 166 . Consistent with some embodiments, NMF decomposition unit  144  may be configured to Fourier transform the first audio signal (e.g., the speech channel signal in  FIG. 1B ) and the second audio signal (e.g., the interference channel signal in  FIG. 1B ) into a frequency domain. The two Fourier transforms can perform in parallel. 
     NMF decomposition unit  144  may be further configured to decompose each Fourier-transformed audio signal using NMF to obtain an NMF basis matrix and an activation matrix. NMF algorithm is a dimension-reduction technique and aims to factorize a nonnegative matrix X∈R I×J , into a product of two nonnegative matrices, X≈TV, where T∈R I×b  are several spectral bases and V∈R b×J  are temporal activations, where I and J denote the numbers of frequency bins and time frames, respectively, and b is the number of basis vectors. Typically, b (I+J)&lt;I×J. T∈R I×b  and V∈R b×J  minimize some divergence metric, d(X, TV). 
     Consistent with some embodiments, each basis matrix T may consist of a speech basis matrix T s  and a noise basis matrix T n , i.e., T=[T s  T n ], while the corresponding activation matrix V=[V s V n ]′ with ′ denoting matrix transpose. In a training stage, T s  and T n  can be trained separately with clean speech and noise data, respectively. At the speech enhancement stage, the basis matrix may be fixed and only activation matrix is updated. In some embodiments, once the algorithm converges, an optimal spectral gain G, i.e., Wiener gain, may be determined based on the speech and noise estimates derived from the NMF analysis, e.g., according to equation (1). 
     
       
         
           
             
               
                 
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     In some embodiments, basis and activation matrices may be updated in a MU procedure according to some cost functions. For example, three special instances of β-divergence may be applied as metrics in MU rules, e.g., Euclidean distance (β=2), Kullback-Leibler (KL) divergence (β=1), and Itakura-Saito (IS) divergence (β=0). In some embodiments, MU rules update basis matrix T and activation matrix V alternatively according to equations (2) and (3). 
     
       
         
           
             
               
                 
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     For example, as shown in  FIG. 1B , NMF decomposition unit  144  may implement module  161  to obtain the NMF speech bases of the separated speech channel signal and implement module  162  to obtain the NMF interference bases of the separated interference channel signal. In some embodiments, if rank-1 MNMF is implemented to separate the multi-channel audio signals as shown in  FIG. 1B , the NMF decomposition does not need to be performed again, but rather can be copied from the MU procedure in rank-1 MNMF. 
     Noise estimation unit  146  may be configured to obtain a modified NMF interference bases in a frequency domain based on the first decomposition data (e.g., the NMF speech bases) and the second decomposition data (e.g., the NMF interference bases). In some embodiments, a third NMF basis matrix corresponding to a noise signal is generated based on a first NMF basis matrix and a second NMF basis matrix. 
     Generally, basis matrix represents the frequency structure of the signal (e.g., harmonics of speech). In the separated speech channel, it is expected that speech related basis has larger value. Frequency sub-bands are labeled as speech if those speech related basis exceeds some pre-defined thresholds. Accordingly, elements of the first NMF basis matrix exceeding a third threshold are considered attributable to a speech component. 
     The corresponding elements of the second NMF basis matrix are then substituted with a predetermined value. The overwritten second NMF basis matrix is saved as a third NMF basis matrix. In some embodiments, in the separated interference channel, NMF basis matrix within the frequency sub-bins labeled above can be set to zero. For example, as shown in  FIG. 1B , noise estimation module  146  may implement module  163  to exclude speech from the interference bases. By doing so, speech component is eliminated from interference basis matrix, and thus speech harmonics and strong unvoiced speech can be preserved. In some embodiments, a noise component in a frequency domain is obtained by using the third NMF basis matrix. 
     Noise estimation unit  146  may be further configured to obtain an estimated noise component (e.g., the reconstructed speech spectrum). In some embodiments, the third NMF basis matrix may be used to reconstruct the first audio signal, by implementing, e.g., module  164  in  FIG. 1B . For example, the modified interference basis matrix (an example of the third NMF basis matrix) is utilized to reconstruct the separated speech spectrum, similar to regular NMF speech enhancing stage. The basis matrix is fixed and only activation matrix is updated. By using the distortion-free speech bases obtained from module  163 , interference magnitude spectrum in the separated speech channel can be estimated. 
     In some embodiments, speech signal enhancing unit  148  may be configured to calculate the Euclidean distances between elements of a Fourier-transformed first audio signal and the corresponding elements of an estimated noise component in a frequency domain. For example, speech signal enhancing unit  148  may implement a module  165  of  FIG. 1B  to calculate the distances between the spectra. In some embodiments, the Euler distance between the reconstructed and speech spectrum is calculated. A large distance may be expected at the speech harmonics and unvoiced speech zone, since interference bases exclude speech information. In some embodiments, distance is calculated on each time-frequency (T-F) bin and then normalized along frequency scales. 
     In some embodiments, speech signal enhancing unit  148  may be further configured to adjust the elements of the Fourier-transformed first audio signal by gains determined based on the respective Euclidean distances. For example, speech signal enhancing unit  148  may implement a module  166  of  FIG. 1B  to calculate the gains. In some embodiments, a sigmoid-like activation function is used to convert the distance into the gain ranged in [0, 1]. For example, a modified version of sigmoid function described by equations (5) and (6) can be used. In the following equations, X i,j  denotes the separated speech spectrum, {circumflex over (X)} i,j  denotes the reconstructed speech spectrum, d i,j  denotes the distance at T-F bin (i,j), and ∥∥ denotes Euclidean norm.
 
 d   i,j   =|X   i,j   −{circumflex over (X)}   i,j |  (5)
 
 d   i,j   =d   i,j   /∥d   i,j ∥  (6)
 
     In some embodiments, speech signal enhancing unit  148  may inverse Fourier transform on the adjusted Fourier-transformed first audio signal to obtain an enhanced audio signal in a time domain. 
     Memory  106  and storage  108  may include any appropriate type of mass storage provided to store any type of information that processor  104  may need to operate. Memory  106  and storage  108  may be a volatile or non-volatile, magnetic, semiconductor, tape, optical, removable, non-removable, or other type of storage device or tangible (i.e., non-transitory) computer-readable medium including, but not limited to, a ROM, a flash memory, a dynamic RAM, and a static RAM. Memory  106  and/or storage  108  may be configured to store one or more computer programs that may be executed by processor  104  to perform noise reducing and audio signal enhancing functions disclosed herein. For example, memory  106  and/or storage  108  may be configured to store program(s) that may be executed by processor  104  to enhance an audio signal acquired from an audio source. 
     Memory  106  and/or storage  108  may be further configured to store information and data used by processor  104 . For instance, memory  106  and/or storage  108  may be configured to store the various types of data (e.g., audio signals, metadata, etc.) acquired by acquisition device  110 . Memory  106  and/or storage  108  may also store intermediate data such as machine learning models, thresholds, and parameters, etc. The various types of data may be stored permanently, removed periodically, or disregarded immediately after each audio signal is processed. 
     Speaker  130  may be configured to output an enhanced audio signal received from communication interface  102 . Speaker  130  may connect to a speech recognition system as an audio input device. In some embodiments, speaker  130  may be a standalone audio display/output device or part of another device, such as a mobile phone, a wearable device, a headphone, a vehicle, a surveillance system, etc. 
       FIG. 2  illustrates a flowchart of an exemplary method  200  for reducing noise in an audio signal, according to embodiments of the disclosure. In some embodiments, method  200  may be implemented by an audio signal enhancement system that includes, among other things, server  120 , acquisition device  110 , and speaker  130 . However, method  200  is not limited to that exemplary embodiment. Method  200  may include steps S 202 -S 212  as described below. It is to be appreciated that some of the steps may be optional to perform the disclosure provided herein. Further, some of the steps may be performed simultaneously, or in a different order than shown in  FIG. 2 . 
     In step S 202 , a multi-channel audio signal is received from acquisition device  110 . In some embodiments, acquisition device  110  may include at least two acquisition channels, or include at least two individual acquisition units, to acquire multi-channel audio signals, such as first-channel signal  103  and second-channel signal  105 . For example, a speech may be acquired by acquisition device  110  in a noisy stadium environment through different microphones. In some embodiments, both channel signals  103  and  105  are mixtures of speech signals and environmental noise signals. The audio information acquired through multiple channels can be later utilized for a blind source separation. Acquisition device  110  sends a first-channel signal  103  and a second-channel signal  105  to communication interface  102 . 
     In step S 204 , processor  104  uses a blind source separation method to separate the multi-channel audio signals acquired from audio source  101 . In some embodiments, multi-channel NMF(MNMF) which is a natural extension of simple NMF method for multi-channel signals may be used to separate the multi-channel audio signals. By utilizing information between channels (e.g., the first-channel audio signal  103  and the second-channel audio signal  105 ), MNMF can cluster the decomposed bases into specific sources in the blind situation. As shown in the example of  FIG. 1B , rank-1 MNMF may be used as a blind source separation method to obtain separated speech and interference channels. Rank-1MNMF separation can be implemented by signal separation unit  142  as shown in  FIG. 1A . The first audio signal (e.g., the separated speech channel) has a higher speech signal ratio than the second audio signal (e.g., the separated interference channel). The second audio signal obtained from the signal separation may include few speech components or may not include any speech components. 
     Referring back to  FIG. 2 , in step S 206 , the first audio signal and the second audio signal are decomposed in a frequency domain. Processing details are shown in  FIG. 3  from steps S 302 -S 308 . In step S 302 , the first audio signal can be Fourier transformed in the frequency domain. The transforming can be implemented in NMF decomposition unit  144  shown in  FIG. 1A . In step S 304 , the second audio signal can be Fourier transformed in the frequency domain. In step S 306 , a first NMF basis matrix is extracted using NMF method based on the Fourier transformed first audio signal from step S 302 . Similarly, in step S 308 , a second NMF basis matrix is extracted using NMF method based on the Fourier transformed second audio signal generated from step S 304 . 
     If NMF decomposition unit  144  shown in  FIG. 1A  includes more than one processing units (e.g., different cores), step S 302  and step  304  can be implemented in parallel as shown in  FIG. 3 . Alternatively, the signals can also be Fourier transformed in sequence. Similarly, step S 306  and step  308  can be implemented in parallel or in sequence. In some embodiments, if the rank-1 MNMF is implemented to separate the speech channel and the noise channel as shown in module  150  of  FIG. 1B , the basis matrices generated under MU rules in module  150  can be reused and steps S 306 -S 308  can be skipped. 
     Referring back to  FIG. 2 , in step S 208 , a noise component may be estimated based on a first NMF basis matrix and a second NMF basis matrix by noise estimation unit  146 . Steps S 402 -S 406  shown in  FIG. 4  provides more details on how to estimate the noise component, as embodiments of step S 208 . In some embodiments, a third threshold is configured to identify elements of the first NMF basis matrix attributable to a speech signal. If an element value of the first NMF basis matrix is greater than or equal to the third threshold, the element is attributable to the speech component. If an element of the first NMF basis matrix is less than the third threshold, the element is not attributable to the speech component. For those attributable elements of the first NMF basis matrix, the corresponding elements of the second NMF basis matrix are substituted with a predetermined value. In some embodiments, the predetermined value is set to be 0. A modified second NMF basis matrix is saved as a third NMF basis matrix. 
     For example, a first NMF basis matrix T 1  and a second NMF basis matrix T 2  may be 3 by 3 matrices. Each row and column have three elements. For example, T 1 =[a 11  a 12  a 13 ; a 21  a 22  a 23 ; a 31  a 32  a 33 ]. T 2 =[b 11  b 12  b 13 ; b 21  b 22  b 23 ; b 31  b 32  b 33 ]. a 13  is the element of a first NMF basis matrix T 1  in the first row and the third column. a 22  is the element of the first NMF basis matrix T 1  in the second row and the second column. Values of a 13  and a 22  are less than a third threshold, and other elements of the first NMF basis matrix T 1  are greater than or equal to the third threshold. The predetermined value is set to 0. A third NMF basis matrix T 3 =[b 11  b 12  0; b 21  0b 23 ; b 31  b 32  b 33 ]. In step S 406  shown in  FIG. 4 , the noise component may be obtained by reconstructing the first NMF matrix using the third NMF basis matrix in the frequency domain. 
     In some special cases, the separated noise channel can include pure noise signals. It does not include any speech signals. In this case, the second NMF basis matrix is used as the third NMF basis matrix to estimate the noise component. 
     Referring back to  FIG. 2 , in step S 210 , the first audio signal is enhanced based on the estimated noise component (e.g., the reconstructed speech spectrum) in the frequency domain. In some embodiments, speech signal enhancing unit  148  may be configured to enhance the first audio signal. Steps S 502 -S 506  shown in  FIG. 5  provide more details of embodiments implementing step S 210 . In step S 502 , Euclidean distances are calculated between elements of a Fourier-transformed first audio signal and the corresponding elements of an estimated noise component in the frequency domain. Euclidean distances indicate speech signal ratios in the Fourier-transformed first audio signal. In some embodiments, distance is calculated on each time-frequency (T-F) bin and then normalized along frequency scales. For example, d i,j =|X 1   i,j −X 3   i,j |, d i,j =d i,j /∥d i ∥ where X 1   i,j  denotes the first audio signal at T-F bin (i,j), X 3   i,j  denotes an estimated noise component at T-F bin (i,j), d i,j  represents the distance at T-F bin (i,j), and ∥∥ is Euclidean norm. 
     Consistent with some embodiments, in step S 504 , gains are calculated based on Euclidean distances. In some embodiments, gains are linearly proportional to the respective Euclidean distances. For example, regularization can be used to obtain gains based on the Euclidean distances and the value of a gain is between 0 and 1. In some embodiments, a sigmoid-like activation function is used to convert the distance into the gain ranged in [0, 1]. 
     In step S 506 , elements of the Fourier-transformed first audio signal generated in step  302  as shown in  FIG. 3  are adjusted by gains. In some embodiments, a new element is a product of an element of the Fourier-transformed first audio signal and the corresponding gain. 
     Referring back to  FIG. 2 , in step S 212 , an enhanced speech signal may be obtained by inverse Fourier transforming an adjusted Fourier-transformed first audio signal from the frequency domain to the time domain. In some embodiments, speech signal enhancing unit  148  implements step S 212  to inverse Fourier transform the adjusted Fourier-transformed first audio signal. 
     Another aspect of the disclosure is directed to a non-transitory computer-readable medium storing instructions which, when executed, cause one or more processors to perform the methods, as discussed above. The computer-readable medium may include volatile or non-volatile, magnetic, semiconductor, tape, optical, removable, non-removable, or other types of computer-readable medium or computer-readable storage devices. For example, the computer-readable medium may be the storage device or the memory module having the computer instructions stored thereon, as disclosed. In some embodiments, the computer-readable medium may be a disc or a flash drive having the computer instructions stored thereon. 
     It will be apparent to those skilled in the art that various modifications and variations can be made to the disclosed system and related methods. Other embodiments will be apparent to those skilled in the art from consideration of the specification and practice of the disclosed system and related methods. 
     It is intended that the specification and examples be considered as exemplary only, with a true scope being indicated by the following claims and their equivalents.