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In this contribution, we consider MUltiple SIgnal Classification (MUSIC)-type algorithm for a non-iterative microwave imaging of small and arbitrary shaped extended anomalies located in a homogeneous media from scattering matrix whose elements are scattering parameters measured at dipole antennas. In order to explain the feasibility of MUSIC in microwave imaging, we investigate mathematical structure of MUSIC by establishing a relationship with an infinite series of Bessel function of integer order and antennas setting. This is based on the representation formula of scattering parameters in the presence of small anomalies and the application of Born approximation. Simulation results using real-data at $f=925$MHz of angular frequency are exhibited to show the feasibility of designed algorithm and to support investigated structure of imaging function., Comment: 21 pages, 14 figures

We apply MUltiple SIgnal Classification (MUSIC) algorithm for the location reconstruction of a set of {two-dimensional circle-like} small inhomogeneities in the limited-aperture inverse scattering problem. Compared with the full- or limited-view inverse scattering problem, the collected multi-static response (MSR) matrix is no more symmetric (thus not Hermitian), and therefore, it is difficult to define the projection operator onto the noise subspace through the traditional approach. With the help of an asymptotic expansion formula in the presence of small inhomogeneities and the structure of the MSR-matrix singular vector associated with nonzero singular values, we define an alternative projection operator onto the noise subspace and the corresponding MUSIC imaging function. To demonstrate the feasibility of the designed MUSIC, we show that the imaging function can be expressed by an infinite series of integer-order Bessel functions of the first kind and the range of incident and observation directions. Furthermore, we identify that the main factors of the imaging function for the permittivity and permeability contrast cases are the Bessel function of order zero and one, respectively. This further implies that the imaging performance significantly depends on the range of incident and observation directions; peaks of large magnitudes appear at the location of inhomogeneities for permittivity contrast case, and for the permeability contrast case, peaks of large magnitudes appear at the location of inhomogeneities when the range of such directions are narrow, while two peaks of large magnitudes appear in the neighborhood of the location of inhomogeneities when the range is wide enough. The numerical simulation results via noise-corrupted synthetic data also show that the designed MUSIC algorithm can address both permittivity and permeability contrast cases., Comment: 26 pages, 10 figures

This study investigates the applicability of Kirchhoff migration (KM) for a fast identification of unknown objects in a real-world limited-aperture inverse scattering problem. To demonstrate the theoretical basis for the applicability including unique determination of objects, the imaging function of the KM was formulated using a uniformly convergent infinite series of Bessel functions of integer order of the first kind based on the integral equation formula for the scattered field. Numerical simulations performed using the experimental Fresnel dataset are exhibited to achieve the theoretical results., Comment: 6 pages, 3 figures

The problem of the real-time microwave imaging of small, moving objects from a scattering matrix, whose elements are measured scattering parameters, without diagonal elements is considered herein. An imaging algorithm based on a Kirchhoff migration operated at single frequency is designed, and its mathematical structure is investigated by establishing a relationship with an infinite series of Bessel functions of integer order and antenna configuration. This is based on the application of the Born approximation to the scattering parameters of small objects. The structure explains the reason for the detection of moving objects via a designed imaging function and supplies its some properties. To demonstrate the strengths and weaknesses of the proposed algorithm, various simulations with real-data are conducted., Comment: 15 pages, 5 figures

Generally, to apply the MUltiple SIgnal Classification (MUSIC) algorithm for the rapid imaging of small inhomogeneities, the complete elements of the multi-static response (MSR) matrix must be collected. However, in real-world applications such as microwave imaging or bistatic measurement configuration, diagonal elements of the MSR matrix are unknown. Nevertheless, it is possible to obtain imaging results using a traditional approach but theoretical reason of the applicability has not been investigated yet. In this paper, we establish mathematical structures of the imaging function of MUSIC from an MSR matrix without diagonal elements in both transverse magnetic (TM) and transverse electric (TE) polarizations. The established structures demonstrate why the shape of the location of small inhomogeneities can be retrieved via MUSIC without the diagonal elements of the MSR matrix. In addition, they reveal the intrinsic properties of imaging and the fundamental limitations. Results of numerical simulations are also provided to support the identified structures., Comment: 20 pages, 7 figures

We consider the application of a subspace migration (SM) algorithm to quickly identify small objects in microwave imaging. In various problems, it is easy to measure the diagonal elements of the scattering matrix if the location of the transmitter and the receiver is the same. To address this issue, several studies have been conducted by setting the diagonal elements to zero. In this paper, we generalize the imaging problem by setting diagonal elements of the scattering matrix as a constant with the application of SM. To show the applicability of SM and its dependence on the constant, we show that the imaging function of SM can be represented in terms of an infinite series of the Bessel functions of integer order, antenna number and arrangement, and applied constant. This result enables us to discover some further properties, including the unique determination of objects. We also demonstrated simulation results with synthetic data to support the theoretical result., Comment: 20 pages, 12 figures

In this study, we consider the application of orthogonality sampling method (OSM) with single and multiple sources for a fast identification of small objects in limited-aperture inverse scattering problem. We first apply the OSM with single source and show that the indicator function with single source can be expressed by the Bessel function of order zero of the first kind, infinite series of Bessel function of nonzero integer order of the first kind, range of signal receiver, and the location of emitter. Based on this result, we explain that the objects can be identified through the OSM with single source but the identification is significantly influenced by the location of source and applied frequency. For a successful improvement, we then consider the OSM with multiple sources. Based on the identified structure of the OSM with single source, we design an indicator function of the OSM with multiple sources and show that it can be expressed by the square of the Bessel function of order zero of the first kind an infinite series of the square of Bessel function of nonzero integer order of the first kind. Based on the theoretical results, we explain that the objects can be identified uniquely through the designed OSM. Several numerical experiments with experimental data provided by the Institute Fresnel demonstrate the pros and cons of the OSM with single source and how the designed OSM with multiple sources behave., Comment: 17 pages, 11 figures

It has been demonstrated that the MUltiple SIgnal Classification (MUSIC) algorithm is fast, stable, and effective for localizing small anomalies in microwave imaging. For the successful application of MUSIC, exact values of permittivity, conductivity, and permeability of the background must be known. If one of these values is unknown, it will fail to identify the location of an anomaly. However, to the best of our knowledge, no explanation of this failure has been provided yet. In this paper, we consider the application of MUSIC to the localization of a small anomaly from scattering parameter data when complete information of the background is not available. Thanks to the framework of the integral equation formulation for the scattering parameter data, an analytical expression of the MUSIC-type imaging function in terms of the infinite series of Bessel functions of integer order is derived. Based on the theoretical result, we confirm that the identification of a small anomaly is significantly affected by the applied values of permittivity and conductivity. However, fortunately, it is possible to recognize the anomaly if the applied value of conductivity is small. Simulation results with synthetic data are reported to demonstrate the theoretical result., Comment: 13 pages, 7 figures

Although the MUltiple SIgnal Classification (MUSIC) algorithm has demonstrated suitability as a microwave imaging technique for detecting anomalies, there is a fundamental limit that it requires a switching device to be used which permits an antenna to transmit and receive signals simultaneously. In this paper, we design a MUSIC-type imaging function using scattering parameter data to find small anomaly and explore its mathematical structure. Considering the investigated structure, we confirm that the imaging performance is highly dependent on the antenna configurations and suggest an arrangement of antennas to enhance imaging performance. Simulation results with synthetic data are displayed to support theoretical result., Comment: 23 pages, 17 figures

Accurately extracting driving events is the way to maximize computational efficiency and anomaly detection performance in the tire frictional nose-based anomaly detection task. This study proposes a concise and highly useful method for improving the precision of the event extraction that is hindered by extra noise such as wind noise, which is difficult to characterize clearly due to its randomness. The core of the proposed method is based on the identification of the road friction sound corresponding to the frequency of interest and removing the opposite characteristics with several frequency filters. Our method enables precision maximization of driving event extraction while improving anomaly detection performance by an average of 8.506%. Therefore, we conclude our method is a practical solution suitable for road surface anomaly detection purposes in outdoor edge computing environments., Comment: 5 pages, 4 figures, 4 tables

We present the result of the Infrared Medium-deep Survey (IMS) $z\sim6$ quasar survey, using the combination of the IMS near-infrared images and the Canada-France-Hawaii Telescope Legacy Survey (CFHTLS) optical images. The traditional color-selection method results in 25 quasar candidates over $86$ deg$^{2}$. We introduce the corrected Akaike Information Criterion (AICc) with the high-redshift quasar and late-type star models to prioritize the candidates efficiently. Among the color-selected candidates, seven plausible candidates finally passed the AICc selection of which three are known quasars at $z\sim6$. The follow-up spectroscopic observations for the remaining four candidates were carried out, and we confirmed that two out of four are $z\sim6$ quasars. With this complete sample, we revisited the quasar space density at $z\sim6$ down to $M_{1450}\sim-23.5$ mag. Our result supports the low quasar space density at the luminosity where the quasar's ultraviolet ionizing emissivity peaks, favoring a minor contribution of quasars to the cosmic reionization., Comment: 21 pages, 13 figures, 4 tables. Accepted for publication in AJ

Many backdoor removal techniques in machine learning models require clean in-distribution data, which may not always be available due to proprietary datasets. Model inversion techniques, often considered privacy threats, can reconstruct realistic training samples, potentially eliminating the need for in-distribution data. Prior attempts to combine backdoor removal and model inversion yielded limited results. Our work is the first to provide a thorough understanding of leveraging model inversion for effective backdoor removal by addressing key questions about reconstructed samples' properties, perceptual similarity, and the potential presence of backdoor triggers. We establish that relying solely on perceptual similarity is insufficient for robust defenses, and the stability of model predictions in response to input and parameter perturbations is also crucial. To tackle this, we introduce a novel bi-level optimization-based framework for model inversion, promoting stability and visual quality. Interestingly, we discover that reconstructed samples from a pre-trained generator's latent space are backdoor-free, even when utilizing signals from a backdoored model. We provide a theoretical analysis to support this finding. Our evaluation demonstrates that our stabilized model inversion technique achieves state-of-the-art backdoor removal performance without clean in-distribution data, matching or surpassing performance using the same amount of clean samples., Comment: Because of an equation and author informational error, this paper has been withdrawn by the submitter