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Some conventional transforms such as Discrete Walsh-Hadamard Transform (DWHT) and Discrete Cosine Transform (DCT) have been widely used as feature extractors in image processing but rarely applied in neural networks. However, we found that…
Ultrasound modulated bioluminescence tomography (UMBLT) is an imaging method which can be formulated as a hybrid inverse source problem. In the regime where light propagation is modeled by a radiative transfer equation, previous approaches…
This paper presents new results in the theory of number theoretic Hilbert (NHT) transforms. New polymorphic solutions have been found for the 14-point and 16-point transforms. Several transform pairs are computed and solutions found for…
In this work we introduce a new Radon transform which arises from a new modality of Compton Scattering Tomography (CST). This new system is made of a single detector rotating around a fixed source. Unlike some previous CST, no collimator is…
We utilize click-counting theory for the reconstruction of photon statistics. Our approach employs an analytic pseudo-inversion method to estimate photon counts from measured click counts. A reconfigurable time-bin multiplexing,…
We introduce single-shot X-ray tomography that aims to estimate the target image from a single cone-beam projection measurement. This linear inverse problem is extremely under-determined since the measurements are far fewer than the number…
The derivation of the time-dependent variational equations of the Multi-Configuration Time-Dependent Hartree (MCTDH) method for high-dimensional quantum propagation is revisited from the perspective of tangent space projection methods. In…
Accurate and efficient algorithms for the inversion of the cumulative central beta distribution are described. The algorithms are based on the combination of a fourth-order fixed point method with good non-local convergence properties (the…
We address the initial source identification problem for the heat equation, a notably ill-posed inverse problem characterized by exponential instability. Departing from classical Tikhonov regularization, we propose a novel approach based on…
The Hilbert-Huang transform (HHT) consists of empirical mode decomposition (EMD), which is a template-free method that represents the combination of different intrinsic modes on a time-frequency map (i.e., the Hilbert spectrum). The…
Eigenvalue transformations, which include solving time-dependent differential equations as a special case, have a wide range of applications in scientific and engineering computation. While quantum algorithms for singular value…
Computed Tomography (CT) is an imaging technique where information about an object are collected at different angles (called projections or scans). Then the cross-sectional image showing the internal structure of the slice is produced by…
A photon is the single excitation of a particular spatiotemporal mode of the electromagnetic field. A precise knowledge of the mode structure is therefore essential for its processing and detection, as well as for applying generic quantum…
A fast inverse heat conduction model (IHCM) is developed for estimating unknown properties of multi-layer composites considering internal heat generation. This work builds on the validated analytical forward models presented in Part I.…
Accurate, low-latency estimates of the instantaneous phase of oscillations are essential for closed-loop sensing and actuation, including (but not limited to) phase-locked neurostimulation and other real-time applications. The…
A novel electromagnetic quantitative inversion scheme for translationally moving targets via phase correlation registration of back-projection (BP) images is proposed. Based on a time division multiplexing multiple-input multiple-output…
Computed Tomography is one of the efficient and vital modalities of non-destructive techniques (NDT). Various factors influence the CT reconstruction result, including limited projection data, detector electronics optimization, background…
An orthogonal 16-point approximate discrete cosine transform (DCT) is introduced. The proposed transform requires neither multiplications nor bit-shifting operations. A fast algorithm based on matrix factorization is introduced, requiring…
The design of the optimal inverse discrete cosine transform (IDCT) to compensate the quantization error is proposed for effective lossy image compression in this work. The forward and inverse DCTs are designed in pair in current image/video…
This paper is concerned with a numerical method for a 3D coefficient inverse problem with phaseless scattering data. These are multi-frequency data generated by a single direction of the incident plane wave. Our numerical procedure consists…