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The manufacturing of light-emitting diodes is a complex semiconductor-manufacturing process, interspersed with different measurements. Among the employed measurements, photoluminescence imaging has several advantages, namely being a…
Changepoint detection is commonly formulated by minimizing the sum of in-sample losses to quantify the model's overall fit. However, for flexible modeling procedures -- especially those involving high-dimensional parameter spaces or…
Full Waveform Inversion (FWI) is an important geophysical technique considered in subsurface property prediction. It solves the inverse problem of predicting high-resolution Earth interior models from seismic data. Traditional FWI methods…
Diverse applications in photonics and microwave engineering require a means of measurement of the instantaneous frequency of a signal. A photonic implementation typically applies an interferometer equipped with three or more output ports to…
Seismic signals are typically compared using travel time difference or $L_2$ difference. We propose the Wasserstein metric as an alternative measure of fidelity or misfit in seismology. It exhibits properties from both of the traditional…
In micro-seismic event measurements, pinpointing the passive source's exact spatial and temporal location is paramount. This research advocates for the combined use of both P- and S-wave data, captured by geophone monitoring systems, to…
In this paper, I will introduce a new form of regression, that can adjust overfitting and underfitting through, "distance-based regression." Overfitting often results in finding false patterns causing inaccurate results, so by having a new…
Deconvolution is a fundamental inverse problem in signal processing and the prototypical model for recovering a signal from its noisy measurement. Nevertheless, the majority of model-based inversion techniques require knowledge on the…
Full-waveform inversion problems are usually formulated as optimization problems, where the forward-wave propagation operator $f$ maps the subsurface velocity structures to seismic signals. The existing computational methods for solving…
Wavelet estimators for a probability density f enjoy many good properties, however they are not "shape-preserving" in the sense that the final estimate may not be non-negative or integrate to unity. A solution to negativity issues may be to…
Defect detection by ultrasonic method is limited by the pulse width. Resolution can be improved through a deconvolution process with a priori information of the pulse or by its estimation. In this paper a regularization of the Wiener filter…
Producing reliable acoustic subsurface velocity models still remains the main bottleneck of the oil and gas industry's traditional imaging sequence. In complex geological settings, the output of conventional ray-based or wave-equation-based…
The details of an image with noise may be restored by removing noise through a suitable image de-noising method. In this research, a new method of image de-noising based on using median filter (MF) in the wavelet domain is proposed and…
We study an inverse problem for the wave equation, concerned with estimating the wave speed, aka velocity, from data gathered by an array of sources and receivers that emit probing signals and measure the resulting waves. The typical…
In many real-world inverse problems, only incomplete measurement data are available for training which can pose a problem for learning a reconstruction function. Indeed, unsupervised learning using a fixed incomplete measurement process is…
In [Engquist et al., Commun. Math. Sci., 14(2016)], the Wasserstein metric was successfully introduced to the full waveform inversion. We apply this method to the earthquake location problem. For this problem, the seismic stations are far…
Deformable convolution, originally proposed for the adaptation to geometric variations of objects, has recently shown compelling performance in aligning multiple frames and is increasingly adopted for video super-resolution. Despite its…
It is known that the continuous wavelet transform of a function $f$ decays very rapidly near the points where $f$ is smooth, while it decays slowly near the irregular points. This property allows one to precisely identify the singular…
Beamforming techniques utilized either at the transmitter or the receiver terminals have achieved superior quality-of-service performances from both the multi-antenna wireless communications systems, communications intelligence and radar…
We study the multivariate deconvolution problem of recovering the distribution of a signal from independent and identically distributed observations additively contaminated with random errors (noise) from a known distribution. For errors…