A radon transform-based method for line spectrum enhancement of vector hydrophone LOFAR spectrograms under low SNR conditions

Abstract

A Line spectrum Enhancement method for LOw Frequency Analysis and Recording (LOFAR) spectrum based on the Radon transform (LELR) is proposed, which is to improve the ability of vector hydrophone spectral line extraction under low signal-to-noise ratio. The LELR method leverages the characteristic that, over long time periods, the line spectra in the LOFAR (Low-Frequency Analysis and Recording) spectrogram approximate straight lines. By exploiting this property, the problem of line spectrum enhancement is transformed into one of linear feature enhancement within the LOFAR spectrogram. This transformation significantly improves the automatic detection and feature recognition capabilities of vector hydrophones. Extensive simulation and sea field experiment results show that the LELR method can effectively solve all kinds of line spectrum problems in actual sea trial data, such as the enhancement and extraction of spectral lines with varying intensities, line spectrum deformation, line spectrum intermittence, even line spectrum damage, etc.

Introduction

The radiated noise of an underwater target is primarily concentrated in the low-frequency and very-low-frequency bands. During propagation, acoustic waves in these frequency ranges are minimally affected by absorption, making them suitable for long-range target detection. However, as the operational frequency decreases, the required array size increases significantly, and the performance of conventional sonar systems becomes insufficient to meet the demands of low- and very-low-frequency detection. The directional response of the vector channel in a vector hydrophone is independent of frequency, enabling high spatial gain even at low and very low frequencies. This characteristic effectively addresses the challenge of the large physical size typically associated with low-frequency sonar systems. Passive detection methods offer strong concealment and broad information acquisition capabilities, allowing for continuous, long-duration monitoring of designated maritime areas. Vector-hydrophone-based passive detection systems—such as submerged markers, communication buoys, and underwater gliders—are widely used to acquire ocean acoustic parameters and detect underwater targets, providing an effective approach for spatial surveillance and control in underwater combat scenarios^1,2. A single vector hydrophone integrates both a pressure sensor channel and a particle velocity sensor channel. Combined processing of these channels enables estimation of target bearing, while the pressure channel alone can be utilized for target feature analysis and classification^3,4.

The radiated noise of underwater targets is primarily concentrated in the low- and very-low-frequency bands. During propagation, acoustic waves at these frequencies are minimally affected by absorption, making them suitable for long-range target detection. However, as the operating frequency decreases, the required array aperture increases substantially, and conventional sonar systems struggle to meet the performance demands of low- and very-low-frequency detection. The directivity of the vector channel in a vector hydrophone is independent of frequency, enabling high spatial gain even at low frequencies. This property effectively addresses the issue of the large physical size associated with low-frequency sonar systems. Passive detection offers strong concealment and high information acquisition capability, allowing for long-term, continuous monitoring of designated maritime areas. Passive detection systems based on vector hydrophones—such as submarine markers, buoys, and underwater gliders—are widely used to acquire ocean acoustic parameters and detect underwater targets, thereby providing an effective means for spatial surveillance and control in underwater combat scenarios. A single vector hydrophone comprises a sound pressure channel and a particle velocity channel. Joint processing of these channels allows for estimation of the target bearing, while the sound pressure channel alone can be used for feature extraction and target classification.

The low-frequency line spectrum components in the radiated noise of underwater targets are characterized by high intensity, good stability, and low propagation loss^5,6,7. The spectral amplitude of low-frequency line spectrum signals is typically 10 dB to 25 dB higher than the average spectral level of the continuous spectrum, attracting considerable attention from researchers in the field of low-noise and stealthy underwater target detection.

Spectrum analysis based on the Discrete Fourier Transform (DFT) remains the primary method for processing radiated noise from underwater targets. Numerous DFT-based or improved line spectrum detection techniques have been developed. Prior to Fast Fourier Transform (FFT) analysis, Adaptive Line Enhancement (ALE) can be employed to enhance the line spectrum components, thereby significantly improving detection gain^8,9. The ALE-based processing method enables adaptive tracking of line spectrum frequency variations within the filter passband, suppresses broadband noise, and produces a relatively flat spectral background, even under non-white or non-stationary noise conditions.

However, in practical data processing, when the input Signal-to-Noise Ratio (SNR) falls below a certain threshold, the processing gain of the system degrades rapidly.

Low Frequency Analysis and Recording (LOFAR) spectrum is a time history diagram of power spectrum obtained by spectral analysis of sound pressure signals, which reflects the power spectrum distribution and changes of signals in time and frequency dimensions. Since the line spectrum in the LOFAR diagram is approximately a straight line, the detection of the line spectrum can be converted into the detection of the line features in the LOFAR diagram, and the corresponding line spectrum enhancement of the signal can be converted into the linear feature enhancement of the LOFAR diagram to improve the detection ability of the line spectrum in the LOFAR diagram.

Improving the detection ability of spectrum lines in LOFAR diagram is helpful for passive sonar target detection, tracking and classification recognition. Successfully extracting spectral lines in LOFAR under low SNR is faced with many challenges:

• (1) To extract spectral lines with low SNR, a low detection threshold must be selected, and the excessive noise points can not thus be removed easily.

• (2) There are signal and background fluctuations and broadband interference, etc., which cause the spectral lines in the LOFAR diagram to be bright and dark, and even there will be many breakpoints in the middle of the spectral lines.

• (3) The dynamic range of both signal and noise is relatively large. Even if the LOFAR spectrum corresponds to the same target, multiple strong and weak spectral lines often coexist.

Since the 1980s until now, spectral line enhancement and automatic extraction in LOFAR spectrum have attracted extensive attention from more scholars with background in image processing, artificial intelligence and statistical signal processing^10,11.

In this paper, a LOFAR spectrum enhancement algorithm based on the combination of Radon transform and Clean algorithm^12,13 is proposed. Simulation research and sea trial data verification research are carried out, which can realize line spectrum enhancement in LOFAR under the condition of low SNR.

Vector hydrophone signal processing

Since the vector hydrophone can effectively obtain the underwater sound pressure and various vector information, a single vector hydrophone can well judge the two-dimensional orientation information of the target. We calculate the azimuth angle of the sound pressure signal and vector signal received by the vector hydrophone. Let x(t), $\theta$ and $\alpha$ represent the sound pressure, the horizontal azimuth angle and the pitch angle, respectively. p(t) is the signal received by the sound pressure channel plus noise. The expressions of sound pressure channel and vibration velocity channel signals are as follows:

$$\begin{aligned} & p(t)=x(t)+n_p (t) \end{aligned}$$

(1)

$$\begin{aligned} & v_x (t)=x(t)cos\theta cos\alpha +n_x (t) \end{aligned}$$

(2)

$$\begin{aligned} & v_y (t)=x(t)sin \theta cos\alpha +n_y (t) \end{aligned}$$

(3)

where $n_p (t)$, $n_x (t)$ and $n_y (t)$ represent the noise of sound pressure channel, the noise of vibration velocity x channel and the noise of vibration velocity y channel, respectively. The average sound intensity is usually used to estimate the azimuth of a single target. Let ${\hat{\theta }}$ denote the estimated azimuth angle of a single target signal, we have

$$\begin{aligned} {{\hat{\theta }}} \mathrm{{ = arctan}}\left( {{\textstyle {{\overline{p(t){v_y}(t)} } \big / {\overline{p(t){v_x}(t)} }}}} \right) \end{aligned}$$

(4)

where $\overline{ p(t){v_y}(t)}$ and $\overline{p(t){v_x}(t)}$ represent the mean of the $p(t){v_y}(t)$ and $p(t){v_x}(t)$, respectively.

When detecting a single target radiating a continuous noise spectrum, the average sound intensity detector performs well. However, in a multi-target environment, the average sound intensity detector can only measure the synthetic sound intensity flow direction of multiple targets, and there is no way to distinguish the multi-target orientation. On the other hand, if the target radiates the line spectrum, the effect of the polyphonic intensifier is far more than that of the average sound intensifier, and it has a good ability to identify and analyze the multi-target orientation with different line spectrum frequencies.

The working principle of the polyphonic intensifier is as follows:

Perform FFT transformation on p(t), $v_x (t)$ and $v_y (t)$ to obtain the corresponding spectrum $P(\omega )$, $V_x (\omega )$ and $V_y (\omega )$. And then, the cross-spectrum of sound pressure and vibration velocity is $S_{pv_x} (\omega )=P(\omega ) V_x^* (\omega )$, $S_{pv_y} (\omega )=P(\omega ) V_y^* (\omega )$.

For the cross-spectrum of sound pressure and vibration velocity, since the sound pressure and vibration velocity are in the same phase, according to the basic characteristics of Fourier transform, the energy of the two inputs in the same phase is concentrated in the real part of the cross-spectrum. Therefore, the energy of the target signal is concentrated in the real part of the cross-spectrum output of the polyphonic intensifier. The imaginary part is mainly interference energy, and the azimuth $\theta (\omega )$ corresponding to each frequency point can be obtained. We have

$$\begin{aligned} \theta (\omega ) = \arctan \left( {{{{{\mathop {\textrm{Re}}\nolimits } \{< P(\omega )V_x^*(\omega )> \} } \over {{\mathop {\textrm{Re}}\nolimits } \{ < P(\omega )V_y^*(\omega ) > \} }}}} \right) \end{aligned}$$

(5)

where $< P(\omega )V_x^*(\omega ) >$ represents the inner product of $P(\omega )$ and $V_x^*(\omega )$, and $< P(\omega )V_y^*(\omega )>$ represents the inner product of $P(\omega )$ and $V_y^*(\omega )$.

The detection systems of marine submersible buoys and underwater gliders usually utilize a single vector hydrophone to estimate the orientation of multiple targets and automatically determine the characteristics of the targets. Line spectrum detection and extraction is a key step. The performance of line spectrum detection and extraction is directly related to the autonomous detection, feature analysis and automatic decision of multi-target in the signal processing system of vector hydrophone.

Line spectrum and line spectrum extraction

The line spectrum characteristics of underwater targets, especially the low frequency line spectrum, are widely used in underwater target monitoring and recognition, and this is because it is suitable for long-distance transmission and contains a large amount of sound source characteristic information.

The simplified form x(t) of underwater target radiation signal can be expressed as:

$$\begin{aligned} x(t) = \sum \nolimits _{n = 1}^N {{A_n} \cdot \cos (2\pi {f_n}t + {\psi _n})} + bs(t) \end{aligned}$$

(6)

where $A_n$ is the modulation amplitude of line spectrum, $f_n$ is the frequency of line spectrum signal, $\Psi _n$ is the random phase of line spectrum signal, t is the time of target radiation signal, bs(t) is the wideband signal, N is the assumed number of independent components. $\Psi _n$ and bs(t) are independent of each other, and $\Psi _n$ is uniformly distributed in the range of $[0\sim 2\pi ]$.

Let

$$\begin{aligned} E[bs(t)]=0, Var[bs(t)]=\sigma _{bs}^2 \end{aligned}$$

(7)

Taking the nth spectrum line in Eq. (1) as an example, the average spectrum level (Spectrum Level Ratio, SLR) of its broadband signal can be calculated as

$$\begin{aligned} (SLR){|_{f = {f_n}}} = 10\lg \left( {\frac{{{\textstyle {{A_n^2} \over 4}}}}{{{\textstyle {{\sigma _{bs}^2} \over {2B}}}}}} \right) = 10\lg \left( {\frac{{B \cdot A_n^2}}{{2\sigma _{bs}^2}}} \right) = 10 \sim 25dB \end{aligned}$$

(8)

where B is the bandwidth of the wideband signa, and lg(.) represents the logarithm with base 10.

In the vector signal processing system, it is necessary for the system to autonomously judge whether there is a line spectrum and give an alarm. Therefore, according to the shape characteristics of line spectrum in power spectrum, a set of line spectrum recognition principles should be determined. On the other hand, a line spectrum must contain both left and right boundaries, and the left and right boundaries cannot exist independently, otherwise both will lose meaning. Therefore, the right side of the left boundary of the line spectrum must be a right boundary, and the left side of the right boundary cannot exist without a left boundary. The shape of the left and right boundaries of the line spectrum should be steep enough, that is, the left and right boundaries should meet certain gradient conditions. The gradient of the left boundary must exceed the positive gradient of the gradient threshold, and the absolute value of the gradient of the right boundary must be greater than the negative gradient of the gradient threshold.

To ensure that the extracted spectral lines are sufficiently narrowband, we impose constraints on the spacing between the left and right edges of a spectral peak. Specifically, when a point satisfying the left-edge condition is detected, a counter is initiated. If the counter exceeds a predefined peak width threshold without encountering a corresponding right-edge point, the previously detected left-edge point is disqualified. However, if a new left-edge candidate appears within the threshold window, it replaces the former candidate, and the counting process restarts. This rule helps accurately define the start and end points of narrowband spectral components.

By applying the above detection logic, we can determine the frequency range of each spectral line. The center frequency of a spectral line is typically chosen as the local maximum within the detected range—i.e., the spectral peak tip. Using this method, the absolute frequency estimation error remains below the spectral resolution $\Delta f$, ensuring high accuracy in identifying narrowband features.

Figure 1a,b present two plots based on vector hydrophone sea trial data: Fig. 1a shows the original power spectrum from the pressure channel, and the second plot displays the extracted line spectra based on the aforementioned detection rules. The horizontal axis represents normalized frequency. In the first plot, it is evident that the energy of the spectral lines is significantly higher than the surrounding broadband noise. However, the amplitude of different line spectra varies considerably across frequencies. To enhance the detection and identification of weak signals, it becomes necessary to amplify these weaker spectral lines. Among common techniques, adaptive line enhancement algorithms are typically employed for this purpose.

Fig. 1

Analysis results of sound pressure channel of vector hydrophone sea trial data.

Adaptive line spectrum enhancement

ALE exploits the characteristic that periodic signals possess a larger coherence radius compared to broadband signals. By introducing a delay to the input signal, the coherence of broadband noise between the original and delayed signals is reduced, while the coherence of the periodic signal is preserved. Subsequently, ALE employs the Least Mean Squares (LMS) algorithm for adaptive filtering. The LMS algorithm aims to minimize the mean squared error of the output by iteratively adjusting the weights of the adaptive filter, thereby achieving optimal matching between the delayed and original signals. Since the broadband interference becomes decorrelated after the delay whereas the periodic components remain correlated, the LMS algorithm can progressively suppress the broadband interference and retain only the periodic components. This process effectively enhances the line spectrum components of the signal.

Assume that the input x(k) is composed of a single-frequency sinusoidal signal s(k) and noise n(k), and the input s(k) is delayed by $\bigtriangleup$ as the reference input of the canceller. Proper selection of $\bigtriangleup$ can de-correlate the noise of the upper and lower channels of the processor, and a single-frequency signal still has a good correlation due to its periodicity. The adaptive filter forms a narrow-band filter whose center frequency is a single-frequency sine frequency. Therefore, the noise component of the delay channel input is suppressed, and the sinusoidal signal component is enhanced, that is, the so-called “adaptive spectral line enhancement”. The principle of adaptive spectral line enhancement is shown in Fig. 2.

Fig. 2

The principle of adaptive spectral line enhancement.

The adaptive line spectrum enhancer generally adopts the transverse filter of LMS operation as the adaptive filter. The basic calculation formulas of the adaptive line spectrum enhancer are as follows:

$$\begin{aligned} & y(k) = \sum \nolimits _i {x(k - \Delta - i)} {w_i}(k) \end{aligned}$$

(9)

$$\begin{aligned} & \varepsilon (k)=x(k)-y(k) \end{aligned}$$

(10)

$$\begin{aligned} & w_i (k)=w_i (k-1)+\mu \varepsilon (k)x(k-\Delta -i) \end{aligned}$$

(11)

$$\begin{aligned} & w_i (0)=0 \end{aligned}$$

(12)

where $\mu$ denotes the adaptive iteration step.

The processing gain of the ALE algorithm is related to the input SNR. Due to the iterative noise, when the input SNR is less than a critical value, the processing gain of the system decreases rapidly. In the actual sea trial data processing, the line spectrum enhancement effect for weak signals is not obvious.

Line spectrum enhancement method for LOFAR spectrum based on radon transform

LOFAR spectrum is an important form of low frequency line spectrum of underwater acoustic target. It is of great significance for passive sonar target detection and recognition to improve the ability of extracting the line in LOFAR. However, due to the complexity of the marine environment, the target line spectrum information is often accompanied by various noise interferences, such as the movement of sea water, the activities of marine life, and the noises made by other ships, etc. All these noises will lead to serious interference of line spectrum in LOFAR spectrum, such as line spectrum crossing, line spectrum deformation, line spectrum intermittence, line spectrum brightness and darkness, and even line spectrum damage.

The traditional line spectrum enhancement research mainly focuses on the adaptive spectrum enhancement of a single batch of data. Since the long-term history of the line spectrum in the LOFAR spectrum is approximately a straight line, based on the azimuth correlation of the underwater moving target track, Radon transform and Radon inverse transform are used to filter the “residual” noise in the accumulated image of the sonar history. The straight line features in the image are preserved, and a more “cleaner” background is thus obtained. The Radon transform is the most effective tool for detecting straight lines in image processing. In this paper, Radon transform is used to transform spectrum line enhancement into linear feature enhancement in LOFAR spectrum.

Radon transform was proposed by scholar Radon in 1917. In image processing technology, Radon transform is widely used in line and curve detection and image reconstruction in image.

In order to overcome the complexity of the filtered back-projection Radon transform algorithm, the forward and inverse Radon transform based on the algebraic method is adopted.

In the cartesian coordinate system, the Radon transform of a discrete line sampled regularly along the X direction can be defined as:

$$\begin{aligned} m(p,\tau ) = \sum \limits _x {g(x,y = \tau + px)} \end{aligned}$$

(13)

where g(x, y) is the data in the (x, y) domain, $m(p,\tau )$ is the data in the $(p,\tau )$ domain, p is the slope of the line centered at the zero offset, and $\tau$ is the intercept time. Both sides of the Eq. (13) are linear, and Fourier transform is performed on both sides of the Eq. (13). After Fourier transform, for each frequency component, we have

$$\begin{aligned} M(p,\omega ) = \sum \limits _x {G(x,\omega )} {e^{j\omega px}} \end{aligned}$$

(14)

For Eq. (14), we rewrite it in matrix form as

$$\begin{aligned} M = LG \end{aligned}$$

(15)

where M denotes the model space, and its dimension is $np \times 1$. G denotes the data space, and its dimension is $nx \times 1$. L denotes the transformation operator, and its dimension is $np \times nx$. Let ${L_{i,k}}$ denote the specific elements of L, we have

$$\begin{aligned} {L_{i,k}} = {e^{j\omega {p_i}{x_k}}} \end{aligned}$$

(16)

The expansion of L matrix is as follows.

$$\begin{aligned} L = \left[ {\begin{array}{*{20}{c}} {{e^{j\omega {p_1}{x_1}}}}& {{e^{j\omega {p_1}{x_2}}}}& { \cdot \cdot \cdot }& {{e^{j\omega {p_1}{x_{nx}}}}}\\ {{e^{j\omega {p_2}{x_1}}}}& {{e^{j\omega {p_2}{x_1}}}}& { \cdot \cdot \cdot }& {{e^{j\omega {p_2}{x_1}}}}\\ { \cdot \cdot \cdot }& { \cdot \cdot \cdot }& { \cdot \cdot \cdot }& { \cdot \cdot \cdot }\\ {{e^{j\omega {p_{np}}{x_1}}}}& {{e^{j\omega {p_{np}}{x_1}}}}& { \cdot \cdot \cdot }& {{e^{j\omega {p_{np}}{x_1}}}} \end{array}} \right] \end{aligned}$$

(17)

Define the inverse Radon transform as follows.

$$\begin{aligned} G = {L^H}M \end{aligned}$$

(18)

Since the forward and reverse Radon transform based on the algebraic method adopts FFT and matrix operations, and the filtered back-projection Radon transform requires three-dimensional search. When the dimension of the image is large, the efficiency of Radon transform based on algebraic method can be greatly improved, and it can be realized in real-time system.

In the LOFAR spectrum, the long time history of the line spectrum is approximately a straight line, therefore it is feasible to use the Radon transform based on the algebraic method to detect the straight line feature of the azimuth history. The Radon transform is sensitive to the linear features in the image, and is called an amplifier of the linear features in the image. Each line in the image plane corresponds to a peak in the transformation plane $(p,\tau )$. Therefore, the detection line features in the image plane are transformed into detection peaks in the transformation plane. An appropriate threshold is used to truncate or enhance the peak value to process the transform plane, and then the inverse Radon transform is adopted to obtain the enhanced image of line features.

When the image SNR is low, there are many lines in the image. And when the energy difference of the straight lines is large, it is difficult to select a suitable threshold in the Radon transform domain. When the threshold is selected larger, the lines with weaker energy will be filtered out. When the threshold is selected smaller, a large amount of noise will be introduced. The inverse Radon transform fails to achieve the purpose of noise suppression. Therefore, an algorithm based on the combination of Radon transform and Clean algorithm^12,13 is proposed, which detects all the lines in the image successively until all the lines in the image are detected. The lines in the image have a large gain in the Radon transform domain. The Clean algorithm is carried out in the Radon transform domain $(p,\tau )$ to separate each bright spot, and thus it has high noise suppression performance.

Clean algorithm was originally proposed by astronomers led by Hogbom. It is a nonlinear image processing algorithm, which aims to fill in some missing image components. Later, some scholars used this idea to estimate the parameters of multi-component Linear Frequency Modulation (LFM) signals in ISAR imaging, which can significantly improve the image quality^13,14,15,16.

Since the strong signal suppresses the weak signal, in the Radon transform domain $(p,\tau )$, directly searching for the maximum peak in the $(p,\tau )$ plane and setting the threshold according to the maximum peak will reduce the estimation accuracy of the weak signals. And in severe cases, the weak signals cannot be recovered. Therefore, following the Clean method, the parameters of the line with the strongest peak value in the $(p,\tau )$ plane are estimated first. And this signal is eliminated from the original signal, and then the second strong component is estimated in the remaining components. Estimated in order from strong to weak, and the specific steps are as follows:

Step One: Perform Radon transform on noisy images.

Step Two: Search for the bright spot with the strongest peak in the $(p,\tau )$ plane, and design the corresponding window function according to the position of the bright spot. Certain prior knowledge is required for the selection of the window function.

Step Three: The bright spots extracted in the $(p,\tau )$ plane are returned to the (x, y) domain by inverse Radon transform.

Step Four: Subtract the image obtained in Step Three from the original noisy image, and then do Radon transform.

Step Five: Return to Step Two to find the bright spot with the strongest peak in the $(p,\tau )$ plane until all bright spots are searched. The number of searches can select a certain threshold or preset a certain number of cycles according to prior knowledge.

Step Six: According to the searched bright spots, the inverse Radon transform can be used to obtain the denoised image of the noisy image.

The key of the above steps is to estimate the parameters $\tau$, p of each line according to the bright spot and to design a window function that matches the bright spot. The window function is designed differently for different bright spot sizes to retain the information of the bright spot as much as possible.

In order to verify the above method, the line spectrum in LOFAR is simulated and processed. The intensities of the three line spectrum are different and the SNR is weak, as shown in Fig. 3. The line spectrum at 40Hz and 50Hz appear intermittent, bright and dark.

Figure 3a shows the LOFAR spectrum with three frequency lines. The positions of the three spectral lines are 40Hz, 50Hz and 100Hz, respectively. The SNRs of the three spectral lines are different. The energy of the spectral line at 100Hz is the strongest, followed by the spectral line at 40Hz, and the spectral line at 50Hz is the weakest. Figure 3b is an image restored by the combination of Radon transform and Clean algorithm. Three spectral lines with different SNR can be accurately extracted. After the line spectrum at 40Hz and 50Hz was processed, the line features became continuous, and the intensity ratio of the three line spectra also remained unchanged. Radon transform, threshold filtering, and inverse Radon transform are used to restore images. If the threshold is set low, the restored image will introduce more noise. On the other hand, if the threshold is set high, weak signals cannot be accurately restored. The combination of Radon transform and Clean algorithm is used to detect successively until all straight lines in the image are detected.

Fig. 3

Radon transform enhanced image.

Performance verification of sea trial data

Moored buoys are essential instruments for acquiring underwater ambient noise data. They are capable of long-term, stable, and autonomous operation in deployed marine areas, enabling the collection of vector acoustic field information as well as synchronous recording of environmental parameters such as pressure, temperature, and compass heading. These capabilities make moored buoys effective for ocean environmental monitoring and underwater target detection and localization. A network of moored buoy observation stations can form a multi-site passive acoustic observation system, which allows for wide-area ocean coverage at relatively low cost. Such distributed systems increase the probability of target detection and provide redundancy in the collected data. This redundancy enables data fusion techniques to be applied, thereby improving the accuracy of target localization. Compared with traditional scalar hydrophone arrays, vector hydrophones can simultaneously capture both acoustic pressure and particle velocity components, as well as directional information of the source. As a result, moored buoy systems equipped with very-low-frequency (VLF) vector hydrophones are becoming increasingly prevalent in oceanographic research and applications.

During the sea test, three vertical array mooring systems equipped with vector hydrophones were deployed to capture the target’s low-frequency line spectrum and bearing information. Each mooring system comprised three vector hydrophones, a connecting cable, a communication buoy, and a seabed anchor. The mooring systems recorded ambient underwater acoustic data via the vector hydrophones and transmitted the data to the experimental vessel through the communication buoys. The structural configuration of the moored detection system is illustrated in Fig. 4.

Fig. 4

LOFAR diagram of sound pressure channel of sea trial data.

During the sea test, the vector hydrophone received the radiated noise of the target and automatically extracted the line spectrum for target direction finding and feature recognition. The data length of the analyzed sound pressure channel exceeded 16 minutes. Due to the long time observation, the features of the line spectrum in the LOFAR diagram could be better analyzed and observed.

Figure 5 shows the LOFAR spectrum of sound pressure channel of single vector hydrophone sea test data. It can be seen from Fig. 5 that in the actual Marine environment, line spectrum interference of moving target, line spectrum deformation, line spectrum drift, line spectrum intermittently, line spectrum bright and dark and so on. These phenomena are not conducive to direction finding and feature discrimination of vector hydrophone. By observing the LOFAR graph, even under the low SNR and complex marine environment interference, the human eye can still easily extract the spectral line from the LOFAR graph. The method proposed in this paper solves the defects of traditional methods better, and the automatic detection and extraction ability of line spectrum is equivalent to that of human eyes.

Figure 6 is the result of line spectrum extraction. Figure 7 is the enhanced graph of Radon transform of LOFAR diagram of sound pressure channel data of vector hydrophone. Figure 8 is the result of line spectrum extraction. Normalized frequencies are adopted for the abscissa in the 4 figures.

The 8 spectral lines selected in Fig. 5 are compared with the image enhanced by Radon transform in Fig. 7. In Fig. 5, the obvious part of the first spectral line lasts for about 400 seconds, and due to the unstable line spectrum, there are discontinuities. In Fig. 6, the continuity of line spectrum extraction results is poor, which affects the target direction finding results. In Fig. 7, the duration of the first line spectrum after enhancement exceeds 1000 seconds. In Fig. 8, the extraction result of the first line spectrum is stable, and the frequency offset can be seen. According to the frequency offset, the doppler frequency shift of the target relative to the potential target can be determined, and the type of the target can be further determined. Moreover, the phenomenon of the second spectral line is similar to that of the first spectral line. After image enhancement, the line spectrum extraction result is obviously better than that of the original LOFAR spectrum. The third spectral line is not obvious in the original LOFAR diagram. After image enhancement, it can be seen from Fig. 7 that the third spectral line is enhanced, and the extraction result of line spectrum is better than that of Fig. 5.

In Fig. 5, the intensities of the 4th and 5th spectral lines are weak, and the spectral extraction results are not shown in Fig. 6. In Fig. 7, the 4th and 5th spectral lines are still visible after enhancement, and the line spectrum in Fig. 8 can be clearly seen. The 6th, 7th and 8th spectral lines in Fig. 5 are weak and not continuous enough, and the line spectrum extraction results in Fig. 6 are poor. After image enhancement, the 6th, 7th and 8th lines in Fig. 8 can still be clearly extracted.

Due to the discontinuity of the line spectrum, the tracking of the spectrum line is affected, and the performance of the vector hydrophone based on the line spectrum direction finding is affected. From Fig. 5, the 9th, 10th and 11th spectral lines with three strong line spectra are selected for comparison. It can be seen from Figs. 5 and 6 that the extraction results of several strong line spectra are discontinuous and intermittent. In Figs. 7 and 8, after image enhancement, the line spectrum extraction results of the 9th, 10th, 10th and 11th spectral lines have been significantly improved.

It can be seen from Figs.  7 and 8 that after the LOFAR line spectrum enhancement and extraction of the line spectrum enhancement, the problems such as line spectrum deformation, line spectrum drift, line spectrum intermittently, line spectrum light and dark are effectively solved, which is more conducive to the automatic decision of the target in the vector hydrophone signal processing system.

Fig. 5

LOFAR diagram of sound pressure channel of sea trial data.

Fig. 6

Line spectrum extraction results of LOFAR.

Fig. 7

LOFAR graph after Radon transform enhancement.

Fig. 8

Line spectrum extracted from enhanced LOFAR graph.

Conclusion

In this paper, a Line spectrum Enhancement method for LOFAR spectrum based on Radon transform (LELR) is proposed, which is to improve the ability of vector hydrophone spectral line extraction under low SNR. The simulation results show that the proposed LELR method can enhance the line spectra effect of multiple lines with different SNR and low SNR, and can significantly improve the detection and extraction ability of line spectrum. The analysis and processing results of sea trial data shows the feasibility of the method, which has a good reference value for the automatic detection and recognition of underwater radiation line spectrum targets using vector hydrophones. The LELR method can not only be used for the enhancement and extraction of the target line spectrum in the LOFAR graph, but also can be directly used to enhance the broadband tone spectrum in the DEMON graph, which is more conducive to the automatic detection and identification of the target.

Although the proposed Radon transform-based method demonstrates promising performance in enhancing and extracting spectral lines from LOFAR spectrograms under low SNR conditions, several limitations remain. First, the performance of the algorithm is sensitive to the selection of Radon transform parameters, which may affect the accuracy of line detection and reconstruction. Second, in scenarios with extremely low signal-to-noise ratios, distinguishing closely spaced spectral lines remains challenging. Third, the method assumes that spectral lines are approximately linear over time; however, in practical environments, target motion or Doppler effects may lead to significant spectral curvature, resulting in reduced enhancement performance. Future research will aim to improve the robustness of the method by introducing adaptive parameter tuning strategies, developing enhanced detection techniques for nonlinearly varying spectral features, and incorporating data-driven approaches to better handle overlapping or intermittent lines in complex acoustic environments.