Related papers: Empirical Evaluation of Typical Sparse Fast Fourie…
Features based on sparse representation, especially using the synthesis dictionary model, have been heavily exploited in signal processing and computer vision. However, synthesis dictionary learning typically involves NP-hard sparse coding…
We consider the problem of recovering signals from their power spectral density. This is a classical problem referred to in literature as the phase retrieval problem, and is of paramount importance in many fields of applied sciences. In…
Recent developments in machine learning and signal processing have resulted in many new techniques that are able to effectively capture the intrinsic yet complex properties of hyperspectral imagery. Tasks ranging from anomaly detection to…
In this paper we consider the special case where a discrete signal ${\bf x}$ of length N is known to vanish outside a support interval of length $m < N$. If the support length $m$ of ${\bf x}$ or a good bound of it is a-priori known we…
The fast Fourier transform (FFT) is undoubtedly an essential primitive that has been applied in various fields of science and engineering. In this paper, we present a decomposition method for parallelization of multi-dimensional FFTs with…
Signal decomposition and multiscale signal analysis provide many useful tools for time-frequency analysis. We proposed a random feature method for analyzing time-series data by constructing a sparse approximation to the spectrogram. The…
Due to excessive need for faster propagations of signals and necessity to reduce number of measurements and rapidly increase efficiency, new sensing theories have been proposed. Conventional sampling approaches that follow Shannon-Nyquist…
The Quantum Fourier Transform (QFT) is a fundamental component of many quantum computing algorithms. In this paper, we present an alternative method for factoring this transformation. Inspired by this approach, we introduce a new quantum…
A compressive sensing (CS) reconstruction method for polynomial phase signals is proposed in this paper. It relies on the Polynomial Fourier transform, which is used to establish a relationship between the observation and sparsity domain.…
In quantum information processing (QIP), the quantum Fourier transform (QFT) has a plethora of applications [1] [2] [3]: Shor's algorithm and phase estimation are just a few well-known examples. Shor's quantum factorization algorithm, one…
We present a matrix-factorization algorithm that scales to input matrices with both huge number of rows and columns. Learned factors may be sparse or dense and/or non-negative, which makes our algorithm suitable for dictionary learning,…
The Number Theoretic Transform (NTT) can be regarded as a variant of the Discrete Fourier Transform. NTT has been quite a powerful mathematical tool in developing Post-Quantum Cryptography and Homomorphic Encryption. The Fourier Transform…
Representing signals with sparse vectors has a wide range of applications that range from image and video coding to shape representation and health monitoring. In many applications with real-time requirements, or that deal with…
In this paper, we study the impact of computational complexity on the throughput limits of the {\color{black}fast Fourier transform (FFT)} algorithm for {\color{black}orthogonal frequency division multiplexing(OFDM)} waveforms. Based on the…
The paper presents a general strategy to solve ordinary differential equations (ODE), where some coefficient depend on the spatial variable and on additional random variables. The approach is based on the application of a recently developed…
The fast Fourier transform (FFT) is one of the most successful numerical algorithms of the 20th century and has found numerous applications in many branches of computational science and engineering. The FFT algorithm can be derived from a…
We present a parallel algorithm for the fast Fourier transform (FFT) in higher dimensions. This algorithm generalizes the cyclic-to-cyclic one-dimensional parallel algorithm to a cyclic-to-cyclic multidimensional parallel algorithm while…
The short-time Fourier transform (STFT) usually computes the same number of frequency components as the frame length while overlapping adjacent time frames by more than half. As a result, the number of components of a spectrogram matrix…
This paper considers the problem of recovering a $k$-sparse, $N$-dimensional complex signal from Fourier magnitude measurements. It proposes a Fourier optics setup such that signal recovery up to a global phase factor is possible with very…
Although Fourier series approximation is ubiquitous in computational physics owing to the Fast Fourier Transform (FFT) algorithm, efficient techniques for the fast evaluation of a three-dimensional truncated Fourier series at a set of…