# Masking of Time-Frequency Patterns in Applications of Passive Underwater Target Detection

- Jüri Sildam
^{1}Email author

**2010**:298038

https://doi.org/10.1155/2010/298038

© Jüri Sildam. 2010

**Received: **6 July 2009

**Accepted: **11 January 2010

**Published: **28 March 2010

## Abstract

Spectrogram analysis of acoustical sounds for underwater target classification is utilized when loud nonstationary interference sources overlap with a signal of interest in time but can be separated in time-frequency ( ) domain. We propose a signal masking method which in a plane combines local statistical and morphological features of the signal of interest. A dissimilarity measure of adjacent cells is used for local estimation of entropy , followed by estimation of entropy difference, where is calculated along the time axis at a mean frequency and is calculated along the frequency axis at a mean time of the window, respectively. Due to a limited number of points used in estimation, the number of possible values, which define a primary mask, is also limited. secondary mask is defined using morphological operators applied to, for example, and . We demonstrate how primary and secondary masks can be used for signal detection and discrimination, respectively. We also show that the proposed approach can be generalized within the framework of Genetic Programming.

## 1. Introduction

In navy applications one needs to intercept and classify pings of an unknown sonar in presence of unknown number and type of interferers. Analyzed signals depending on duration in time ( ) and extent in frequency ( ) are divided into two broad categories: narrow-band ( ) ( ) and broad-band (BB) ( ). Passive detection of signals with and components is usually based on separate approaches (see, e.g., [1]). Typical waveforms in active sonar surveillance are continuous waveform at a constant frequency and amplitude, and frequency modulated waveform. These waveforms are also relevant in passive acoustical analysis, for example, in ping interception and classification. Appearance of these signals in spectrograms depends on the temporal extent of data which is used to estimate a single periodogram, on the amount of overlapping periodograms, and on the weighting window.

After defining the time-frequency ( ) parameters required for spectrogram processing, and general expectation about expected signals, one has to answer the question: what features of detected and signals are sufficient for a target classification? Extended feature analysis is required for analysis of active echoes to discriminate between targets and clutter. A sound timbre is an example of a perception-based feature (see, e.g., [2]). However, in the case of strong interfering signals, or in the case of limited number of sensors (e.g., single sensor), isolation of the full signature of a target may not be possible. In such a case one may try to characterize the detected energy peaks locally, that is, not just by the frequency of detected signal peak and its amplitude but also by spectral energy distribution in close proximity of the detected peak. Classification of spectral peaks is addressed in [3, 4]. Moreover, [5] performed spectrogram segmentation by deciding whether each spectrogram point ( coefficient) belongs to some deterministic component region or to noise (or background) region. They pointed out that to perform such a decision one needs more than the energy level. The authors chose to utilize local statistical features so that these features aggregated in feature space.

The present approach also concentrates on local cell statistics of an input spectrogram image . We are interested in testing for presence of a signal of interest ( ) in a given cell regardless of a number and type of waveforms of interfering sources ( ).

We use two basic assumptions: ( ) and most of the time do not overlap in space; ( ) both and exhibit a high .

Typically in active radar/sonar applications a non-parametric approach is used when one hopes to create a simple detector which is insensitive to environment at a cost of some deterioration in performance as compared to the detectors optimal in Neyman-Pearson sense [6–8]. Since in our case the number and type of waveforms of may change, we approach this problem in the framework of machine learning of one class classification [9, 10]. However, as opposed to the machine learning approaches (e.g., support vector machine or neural networks which put out complex classifiers and are prone to over-fitting), we propose a simple two-step approach. It combines statistical processing and morphological operations to obtain time-frequency masks of . We show that the simplicity of our approach lies in the fact that even after visual inspection of images of proposed features, it is possible to construct masks which can be used for masking and discrimination of . Moreover, we show that the proposed interactive feature selection and construction of masking rules can easily be generalized in a framework of Genetic Programming (GP) [11].

The proposed approach will be described in Section 2. Section 3 will present examples of the proposed approach. While the first three examples will show details of the approach where feature manipulation is based on visual image inspection, the last example will present performance measures over a wide range of peak-to-peak ratios based on a mask created using GP. Finally, a summary and conclusions will be given.

## 2. Approach

### 2.1. Overview

The approach consists basically from two steps: the statistical image processing of one or more spectrograms (Figure 1A) and the construction of masks that comprise feature selection and their combination using some heuristic rules (Figures 1B and 1C). More than one spectrogram may be needed for inspection of feature images under changing environment. At the end of this section we show that a combination of features and heuristic rules can be presented in a form of a syntax tree of GP, which provides a framework for generalization of masking.

The first part of statistical processing is based on the Maximum Mean Discrepancy test ( ) which is carried out on a pair of cells within a sliding window. By moving the window at maximum time and frequency resolution, correlated estimates of dissimilarity of cells are obtained. To estimate the information content of distribution (Figure 1A), the local entropies and which differ in their support, respectively, are calculated. As a result the six images (the reason for six instead of three images will be apparent from the next section) of the features of estimated spectrogram are used to define a set of feature vectors (Figure 1B).

### 2.2. Maximum Mean Discrepancy

*dissimilarity*) on a pair of adjacent time-frequency cells in a window with a predefined time and frequency support. We apply this test to quantify dissimilarity of neighboring cells. Theoretical background and details about the test can be found in [12]. An empirical biased estimate of defined for the pair of cells, centered at , and , , respectively, can be written as

### 2.3. Entropy Estimation

### 2.4. Construction of Time-Frequency Masks

#### 2.4.1. Visual Analysis

In the next subsection we will point out a way to generalize the construction of masks given above.

#### 2.4.2. Genetic Programming

In Genetic Programming programs are represented as syntax trees. A tree includes nodes, which indicate instructions to execute, and links which point to inputs (or terminals) used for execution of instructions [11]. Initially a random set (or population) of trees (or programs) is created and executed recursively following chosen instructions. Using some fitness measure on results of program execution, only a few programs are selected which are then used to generate new programs using some predefined genetic operations. Selection of the fittest programs followed by genetic generation of new programs is repeated until some predefined criteria are met. The final result is given in a form of syntax tree.

## 3. Algorithm Development and Application

### 3.1. Construction of Masks Using Visual Analysis

All given examples consider the case when only a single sensor is available for recording of acoustical data. We construct two masks: primary and secondary. By applying the primary mask, we expect to detect the signals of interest along with the interfering signals. The secondary morphological mask is used then to discriminate between a deterministic , random Gaussian, and interfering signals. Three cases will be considered. The first case simulates a deterministic damped sinusoidal signal against a background of weaker random Gaussian interference and recurring BB signals (e.g., modeling pings of own ship echo-sounder). In the second, a more difficult case, the situation is reverse. Now the interference is stronger than the recurring signal of interest at the background of uniform noise and recurring signal. Finally, a recording of a bird song [15] will be considered. We chose the bird song instead of, for example, marine mammal because the corresponding file is accessible from the Internet, so that the interested parties can carry out similar calculations using the same data. The bird song example also exhibited a mixture of and features, from which we were able to extract components.

- (1)
- (2)
- (3)

where superscript implies a matrix transpose. While in the first (strong signal) and the third (bird call) cases different combinations of secondary masking gave quite consistent results with different choices of a secondary mask, in the case of the second experiment with strong interference and weak signal the results of false alarm reduction were sensitive to the choice of the secondary mask. In general one can see that the primary masks worked well for detection of signal of interest in all three experiments.

Visual inspection shows that in the first experiment most of the NB signals were detected, while BB interference remained undetected as required (except the bottom row, shown by a continuous black line, which was related to the reduced number of grid points at the beginning of masking). However, in the second experiment the BB lines can be clearly seen in Figures 5(e) and 5(h). One should recall that since the signal of interest was on a border line between NB and BB signals, for experiments one and two we used a combination of and tests. In the third experiment however, we used a combination of and tests to derive the primary masks. In this case, already the first primary mask was useful for detection of bird call vocalization around 4200 and 6200 Hz. The secondary mask performed simple dilation of the masked data. In the first experiment, the secondary mask successfully masked interfering signals. The second experiment was the most difficult case. In addition to the secondary mask, a median filter was applied, calculated as an absolute difference between median and values estimated for each row of the spectrogram. The rows with the respective difference higher than 0.05 were set to zero. As a result, dominant detections were observed as expected at 7500 Hz. In the next section we will show that significant reduction of false alarms can be achieved via mask construction in the framework of GP.

### 3.2. Performance and Automation of Masking of Time-Frequency Patterns

To evaluate masking performance we modified previously described simulation so that now it incorporated changing of signal of interest. Each run that lasted about 10 seconds and that was carried out at constant was repeated 50 times. Then the was increased and another 50 runs were performed. Ten different SNR values were used. The range of SNRs values was chosen so that ratio of maximums of spectral peaks of and ( ) changed roughly from to 5 dB. Since was deterministic, the number of peaks over 10 second period was constant and equaled to 19. To eliminate redundancy in a number of masked peaks, the respective peaks were clustered using kd-tree closest point search method. The detection probability ( ) was defined as a ratio between the number of detected (masked) clustered peaks and the true number of peaks, and the false alarm probability was defined as a ratio between of the number of incorrect and number of detected clustered peaks.

To automate masking of patterns we used an open source Matlab GP toolbox [17]. According to Koza [11], a single set-up of governing parameters of GP can be used to address a wide range of problems. The toolbox's demo script "demoparity.m" was adopted to accommodate for the format of input features vectors and for a list of functions. After these changes, we were able successfully automate pattern masking.

The feature vectors centered at a pixel were defined as , where, for example, the first six members were . The transposed feature vectors formed a matrix with a row labeled by or by depending on presence or absence of , respectively. The set of Matlab functions used by GP was . The number of populations was set to 350 and program was stopped after 20 generations.

For automated creation of a mask we used 10 spectrograms, each corresponding to a different . The respective spectrograms were processed following the proposed approach (Figure 1). To show the improvement gained by automation of TF masking of , we compare the respective results with the results obtained by processing of the same data set using a combination of two primary masks. The masks were constructed using a three by three pixels matrix of centered at a given time and frequency of obtained at and 0 dB PPR, respectively. Presence of was declared when either of the primary masks matched exactly underlying pattern of .

### 3.3. Qualitative Comparison of the Proposed Approach to Other Approaches

The first part of this work separated the problem of signal detection and discrimination into two parts, respectively, by defining primary and secondary masks. Finally we showed that both of these problems could be addressed within a single framework of GP.

Separating the problem into two steps is useful in showing how preliminary information can be incorporated into the construction of feature vectors. In this work we assumed that all signals can be presented in one of the two categories: either NB or BB signals. The statistical MMD test followed by estimation of entropies capitalized on this idea by producing features , , and . Clearly the proposed use of MMD test is not the only test that can be used for signal detection in spectrograms. In cases when one has an ability to analyze recorded data over time periods sufficient for track detection, or when signal detection is a part of a tracking approach, a number of approaches can be used for track detection. A recent overview of track detection in spectrograms is given in [18]. More research is required to understand how information gained during signal or track detection can be used for signal or track discrimination. Therefore approaches developed for track detection in spectrograms (e.g., active contour models [19], reassignment, Radon [20] and Hough [21] transforms, simple thresholding) should be complemented by statistical information (e.g., higher statistical moments) obtained in close proximity of detected time-frequency tracks. Additionally, the features based on cepstral processing may be used when one is working with quasiperiodic signals, for example, sonar pings.

For purposes of this work, postprocessing of collected data implicitly provided statistical and morphological information mainly about signal of interest. Since a number and type of interfering sources were assumed to be unknown, the presented problem can be treated as a one-class classification or novelty detection problem. Presented results show that by combining statistical and morphological approaches it is possible to reduce false alarms without the reduction of signal detection rate. It is interesting to note that recently in active sonar measurements the authors of [22] were able to reduce significantly false target detections due to clutter using the two-step statistical-morphological processing.

Finally, it should be noted that the computational complexity of MMD test (1) is the highest among all processing blocks involved in masking of the test data.

## 4. Summary and Conclusions

A new approach has been presented for binary masking of signal of interest in presence of narrow-band and broadband interferences in spectrograms. All computations of dissimilarities of TF cells and related entropies required for a binary mask estimation were local in time-frequency space. Rather than thresholding spectrogram data, or related dissimilarity or entropy distributions, the number of grid points used in estimation of entropies and their differences was limited. As a result, the number of values of the respective differences was limited, and these were used to define the primary binary masks, which did not require use of any thresholds for their estimation. An advantage of using dissimilarity rather than spectral energy distribution for entropy estimation was in the known scaling of , which allowed predefinition of the histogram bin limits. We have shown that while local entropy differences calculated from the distribution is an effective way for general signal detection (including interfering signals), then morphological operations can be used to reduce false alarms due to interfering signals. The division of the proposed masking approach into primary and secondary masks is useful if one has to make a distinction between the signal detection and discrimination, or during the interactive construction of signal discrimination processing flow. The presented approach is flexible and can be adopted depending on the underlying problem within a framework of Genetic Programming which unifies the proposed construction of two masks.

## Declarations

### Acknowledgment

A part of this work was supported by the NATO Underwater Research Centre.

## Authors’ Affiliations

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