Related papers: Teaching the concept of convolution and correlatio…
Both of Wavelet and Fast Fourier Transform are strong signal processing tools in the field of Data Analysis. In this paper fast fourier transform (FFT) and Wavelet Transform are employed to observe some important features of Solar image…
The concept of the analytic signal is extended from the case of a real signal with a complex analytic signal to a complex signal with a hypercomplex analytic signal (which we call a hyperanalytic signal) The hyperanalytic signal may be…
To study the processes and mechanisms of the correlation between space and time, particularly between lengths and durations in human perception, a special method (device and procedure) to conduct this experiment was designed and called LDR…
This paper determines how to define a discretely implemented Fourier transform when analysing an observed spatial point process. To develop this transform we answer four questions; first what is the natural definition of a Fourier…
Ptychography involves a sample being illuminated by a coherent, localised probe of illumination. When the probe interacts with the sample, the light is diffracted and a diffraction pattern is detected. Then the probe or sample is shifted…
Motion is a salient cue to recognize actions in video. Modern action recognition models leverage motion information either explicitly by using optical flow as input or implicitly by means of 3D convolutional filters that simultaneously…
Learning physical simulations has been an essential and central aspect of many recent research efforts in machine learning, particularly for Navier-Stokes-based fluid mechanics. Classic numerical solvers have traditionally been…
In this paper we study the scale-space classification of signals via the maximal set of kernels. We use a geometric approach which arises naturally when we consider parameter variations in scale-space. We derive the Fourier transform…
Simulating the radar illumination of large scenes generally relies on a geometric model of light transport which largely ignores prominent wave effects. This can be remedied through coherence ray-tracing, but this requires the Wigner…
State-of-the-art methods for Convolutional Sparse Coding usually employ Fourier-domain solvers in order to speed up the convolution operators. However, this approach is not without shortcomings. For example, Fourier-domain representations…
A new type of an optical interferometer is discussed the phase difference between the interfering beams in which is substantially wavelength dependent. It is shown that the function measured with this device is an integral transform of the…
This paper introduces the concept of on-chip temporal optical computing, based on dispersive Fourier transform and suitably designed modulation module, to perform mathematical operations of interest, such as differentiation, integration, or…
Signal analysis on graphs relies heavily on the graph Fourier transform, which is defined as the projection of a signal onto an eigenbasis of the associated shift operator. Large graphs of similar structure may be represented by a graphon.…
The event camera, benefiting from its high dynamic range and low latency, provides performance gain for low-light image enhancement. Unlike frame-based cameras, it records intensity changes with extremely high temporal resolution, capturing…
Understanding temporal dynamics of video is an essential aspect of learning better video representations. Recently, transformer-based architectural designs have been extensively explored for video tasks due to their capability to capture…
Correlation filters take advantage of specific properties in the Fourier domain allowing them to be estimated efficiently: O(NDlogD) in the frequency domain, versus O(D^3 + ND^2) spatially where D is signal length, and N is the number of…
We generalize the definition of convolution of vectors and tensors on the 2-sphere, and prove that it commutes with differential operators. Moreover, vectors and tensors that are normal/tangent to the spherical surface remain so after the…
This paper examines the existence and region of convergence of Fourier transform of the functions of bicomplex variables with the help of projection on its idempotent components as auxiliary complex planes. Several basic properties of this…
The algorithm behind the Fast Fourier Transform has a simple yet beautiful geometric interpretation that is often lost in translation in a classroom. This article provides a visual perspective which aims to capture the essence of it.
Coherence and correlations represent two related properties of a compound system. The system can be, for instance, the polarization of a photon, which forms part of a polarization-entangled two-photon state, or the spatial shape of a…