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A joint frame and carrier frequency synchronization algorithm for coherent optical systems, based on the digital computation of the fractional Fourier transform (FRFT), is proposed. The algorithm utilizes the characteristics of energy…
Low-count positron emission tomography (PET) reconstruction is a challenging inverse problem due to severe degradations arising from Poisson noise, photon scarcity, and attenuation correction errors. Existing deep learning methods typically…
Convolution and cross-correlation are the basis of filtering and pattern or template matching in multimedia signal processing. We propose two throughput scaling options for any one-dimensional convolution kernel in programmable processors…
The synchrosqueezing transform, a kind of reassignment method, aims to sharpen the time-frequency representation and to separate the components of a multicomponent non-stationary signal. In this paper, we consider the short-time Fourier…
The use of Fourier methods in wave-front reconstruction can significantly reduce the computation time for large telescopes with a high number of degrees of freedom. However, Fourier algorithms for discrete data require a rectangular data…
Bayesian inference, while foundational to probabilistic reasoning, is often hampered by the computational intractability of posterior distributions, particularly through the challenging evidence integral. Conventional approaches like Markov…
The object of this work is to design an adequate regularization for the problem of recovering missing Fourier coefficients, particularly in some non standard situations were low frequency coefficients are lost. In the framework of non-local…
Much work over the last 25 years has demonstrated that the interface-specific, alloptical technique, vibrational sum frequency generation (v-SFG) spectroscopy, is often uniquely capable of characterizing the structure and dynamics of…
The stepped-frequency (SF) waveform is an effective way to achieve high range resolution (HRR) in modern radars. In this paper, we determine some fundamental limits of SF waveforms on ambiguity, stability and accuracy of stable targets…
In many applications in compressed sensing, the measurement matrix is a Fourier matrix, i.e., it measures the Fourier transform of the underlying signal at some specified `base' frequencies $\{u_i\}_{i=1}^M$, where $M$ is the number of…
We consider the classical 1D phase retrieval problem. In order to overcome the difficulties associated with phase retrieval from measurements of the Fourier magnitude, we treat recovery from the magnitude of the short-time Fourier transform…
In this paper, a novel and robust algorithm is proposed for adaptive beamforming based on the idea of reconstructing the autocorrelation sequence (ACS) of a random process from a set of measured data. This is obtained from the first column…
In this paper a sublinear time algorithm is presented for the reconstruction of functions that can be represented by just few out of a potentially large candidate set of Fourier basis functions in high spatial dimensions, a so-called…
This report proposes to discuss the Fourier domain analysis performances of a RESPER probe. A uniform ADC, which is characterized by a sensible phase inaccuracy depending on frequency, is connected to a Fast Fourier Transform (FFT)…
We consider the frequency response problem and derive a posteriori error estimates for the discrete error in a reduced finite element model obtained using the component mode synthesis (CMS) method. We provide estimates in a linear quantity…
Fourier ptychography is a recently explored imaging method for overcoming the diffraction limit of conventional cameras with applications in microscopy and yielding high-resolution images. In order to splice together low-resolution images…
Quarter sampling is a novel sensor design that allows for an acquisition of higher resolution images without increasing the number of pixels. When being used for video data, one out of four pixels is measured in each frame. Effectively,…
Computing the Sparse Fast Fourier Transform(sFFT) of a K-sparse signal of size N has emerged as a critical topic for a long time. The sFFT algorithms decrease the runtime and sampling complexity by taking advantage of the signal inherent…
Lensless imaging methods that account for partial coherence have become very common in the past decade. However, there are no metrics in use for comparing partially coherent light fields, despite the widespread use of such metrics to…
Phasor measurement units (PMUs) are widely used for sub-synchronous oscillation monitoring, yet the effect of windowed discrete Fourier transform (DFT)-based phasor estimation on oscillation observability is not fully characterized. This…