Related papers: Discrete Linear Canonical Transform Based on Hyper…
An orthogonal approximation for the 8-point discrete cosine transform (DCT) is introduced. The proposed transformation matrix contains only zeros and ones; multiplications and bit-shift operations are absent. Close spectral behavior…
The log canonical threshold (lct) is a fundamental invariant in birational geometry, essential for understanding the complexity of singularities in algebraic varieties. Its real counterpart, the real log canonical threshold (rlct), also…
An integrated photonic circuit architecture to perform a modified-convolution operation based on the Discrete Fractional Fourier Transform (DFrFT) is introduced. This is accomplished by utilizing two nonuniformly-coupled waveguide lattices…
Quaternionic Linear Canonical Transforms (QLCTs) are a family of integral transforms, which generalized the quaternionic Fourier transform and quaternionic fractional Fourier transform. In this paper, we extend the energy concentration…
Descriptive region features extracted by object detection networks have played an important role in the recent advancements of image captioning. However, they are still criticized for the lack of contextual information and fine-grained…
This work builds on an existing model of discrete canonical evolution and applies it to the general case of a linear dynamical system, i.e., a finite-dimensional system with configuration space isomorphic to $ \mathbb{R}^{q} $ and linear…
Recently, it was shown that a communication system could be represented as a deep learning (DL) autoencoder. Inspired by this idea, we target the problem of OFDM-based wireless cross-technology communication (CTC) where both in-technology…
This paper is devoted to a discussion of the Discrete Fourier Transform (DFT) representation of a chaotic finite-duration sequence. This representation has the advantage that is itself a finite-duration sequence corresponding to samples…
Fourier representations play a central role in operator learning methods for partial differential equations and are increasingly being explored in quantum machine learning architectures. The classical fast Fourier transform (FFT),…
A model, called the linear transform network (LTN), is proposed to analyze the compression and estimation of correlated signals transmitted over directed acyclic graphs (DAGs). An LTN is a DAG network with multiple source and receiver…
Low Dose Computed Tomography (LDCT) is widely used as an imaging solution to aid diagnosis and other clinical tasks. However, this comes at the price of a deterioration in image quality due to the low dose of radiation used to reduce the…
In deep time series forecasting, the Fourier Transform (FT) is extensively employed for frequency representation learning. However, it often struggles in capturing multi-scale, time-sensitive patterns. Although the Wavelet Transform (WT)…
Based on the definition of the Fourier transform in terms of the number operator of the quantum harmonic oscillator and in the corresponding definition of the fractional Fourier transform, we have obtained the discrete fractional Fourier…
Convolutional neural networks (CNNs) learn filters in order to capture local correlation patterns in feature space. We propose to learn these filters as combinations of preset spectral filters defined by the Discrete Cosine Transform (DCT).…
Decoder-only transformers have become the standard architecture for large language models (LLMs) due to their strong performance. Recent studies suggest that, in pre-trained LLMs, early, middle, and late layers may serve distinct roles:…
Graph filtering is a fundamental tool in graph signal processing. Polynomial graph filters (PGFs), defined as polynomials of a fundamental graph operator, can be implemented in the vertex domain, and usually have a lower complexity than…
The unification of understanding and generation within a single multi-modal large model (MLLM) remains one significant challenge, largely due to the dichotomy between continuous and discrete visual tokenizations. Continuous tokenizer (CT)…
Computed tomography (CT) is one of the modalities for effective lung cancer screening, diagnosis, treatment, and prognosis. The features extracted from CT images are now used to quantify spatial and temporal variations in tumors. However,…
Recently, numerous algorithms have been developed to tackle the problem of light field super-resolution (LFSR), i.e., super-resolving low-resolution light fields to gain high-resolution views. Despite delivering encouraging results, these…
Linear combination of Hamiltonian simulation (LCHS) connects the general linear non-unitary dynamics with unitary operators and serves as the mathematical backbone of designing near-optimal quantum linear differential equation algorithms.…