Joint Fourier Transform Research Articles

Irregular surface temperature monitoring in liver procurement via time-vertex signal processing

The liver viability monitoring during its procurement is critical to guarantee the safe liver transportation. Traditionally, the viability is assessed by taking invasive biopsy on the liver surface. Recently, the noninvasive thermal images of liver surface have been used as an alternative assessment way. Researchers have proposed monitoring and classification approaches based on the thermal images. Existing works have demonstrated the importance of the temporal variation or the spatial variation of the thermal images to the viability monitoring. However, there is no prior work to leverage the graph structure of the spatio-temporal processes for the viability monitoring. In this paper, we propose a time-vertex signal processing framework for the irregular thermal data of the pure liver region monitoring. In particular, we extract features of irregular thermal data based on the joint Fourier transform (JFT), which is an integration of graph Fourier transform (GFT) and discrete Fourier transform (DFT). The extracted JFT features can accurately reconstruct the thermal images with a limited number of features. Then, we use a non-parametric online change-point estimation method, based on online scan B statistics, to monitor the JFT features without a parametric distribution. Our proposed framework is applied to both simulation and the liver procurement data, and achieves good monitoring performance.

Fourier analysis on robustness of graph convolutional neural networks for skeleton-based action recognition

Using Fourier analysis, we explore the robustness and vulnerability of graph convolutional neural networks (GCNs) for skeleton-based action recognition. We adopt a joint Fourier transform (JFT), a combination of the graph Fourier transform (GFT) and the discrete Fourier transform (DFT), to examine the robustness of adversarially-trained GCNs against adversarial attacks and common corruptions. Experimental results with the NTU RGB+D dataset reveal that adversarial training does not introduce a robustness trade-off between adversarial attacks and low-frequency perturbations, which typically occurs during image classification based on convolutional neural networks. This finding indicates that adversarial training is a practical approach to enhancing robustness against adversarial attacks and common corruptions in skeleton-based action recognition. Furthermore, we find that the Fourier approach cannot explain vulnerability against skeletal part occlusion corruption, which highlights its limitations. These findings extend our understanding of the robustness of GCNs, potentially guiding the development of more robust learning methods for skeleton-based action recognition.

Joint transform correlator subtracting a modified Fourier spectrum

The optically generated joint Fourier transform (JFT) of a test image and a reference image is processed using a new method: the JFT is recorded twice. In the second recording the reference image is phase shifted by π with respect to the first recording. The two JFT's are subtracted and binarized with a threshold of zero. Strong correlation peaks are obtained, and correlations within the test image are suppressed. Some results of optical implementation are presented, using a ferroelectric liquid crystal display with 128 × 128 pixels for data input. The phase shift of the reference was implemented by the contrast-inverted reference input on the binary light-modulating device. Processing of the JFT is done by a CCD camera, a frame grabber, and a personal computer.

Filter-feature-based rotation-invariant joint Fourier transform correlator

Rotation-invariant target detection using a trained filter-feature-based joint Fourier transform (JFT) correlator is investigated. First, a composite reference image is obtained from a training set of targets. An optimum filter formulation is then applied on this composite image to come up with a new feature that we refer to as a filter feature. This feature is then used in a JFT correlator, which results in a simple and robust rotation-invariant target recognition system.

Coherent Optical Texture Recognition of Digital Ultrasonic Images

Absrracf-Two methods for coherent optical correlation have been applied to liver echotexture recognition and classification. The first method is a multiple holographic filtering. The Fourier transforms of transparencies of normal and pathological samples are stored in a holographic plate, which is used for filtering the images to be classified. The output is the correlation pattern of the reference and the unknown images: the reference texture more similar to the testing one is defined by the brighter correlation peak. Using this method a diagnostic accuracy greater than 90 percent is achieved. The second method is a joint Fourier transform (JFT) correlation. An all-optical and a digital-optical technique have been developed. This last gives the same diagnostic accuracy of the holographic method. Its higher flexibility makes it a promising technique for routine evaluation of liver parenchyma.

Dual-axis joint-Fourier-transform correlator

Theory and experimental results of a dual-axis joint-Fourier-transform (JFT) optical correlator are reported. The correlator is capable of recording large-carrier-frequency holograms of signals with a large space-bandwidth product. Experimental demonstration is carried out using the thermoplastic device as the JFT hologram-recording medium.