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Upsampling

Upsampling

Managing signal sampling rates is essential in digital signal processing to maintain signal integrity. A decimated signal, characterized by a reduced frequency range due to its lower sampling rate, can be upsampled by inserting zeros between each sample. This upsampling process expands the original spectrum and introduces repeated spectral replicas at intervals dictated by the new Nyquist frequency. To refine this zero-inserted sequence, it is passed through a lowpass filter with a cutoff...

Sampling Theorem

Sampling Theorem

In signal processing, the analysis of continuous-time signals, denoted as x(t), often involves sampling techniques to convert these signals into discrete-time signals. This process is essential for digital representation and manipulation. A critical component in sampling is the train of impulses, characterized by the sampling interval and the sampling frequency. The relationship between these parameters and the original signal's properties dictates the success of the sampling process.

Bandpass Sampling

Bandpass Sampling

In signal processing, bandpass sampling is an effective technique for sampling signals that have most of their energy concentrated within a narrow frequency band. This type of signal is known as a bandpass signal. The key principle of bandpass sampling involves sampling the signal at a rate that is greater than twice the signal's bandwidth to prevent aliasing.
A bandpass signal has a spectrum with a lower frequency limit, denoted as ω1, and an upper frequency limit, denoted as ω2....

Sampling Continuous Time Signal

Sampling Continuous Time Signal

In signal processing, a continuous-time signal can be sampled using an impulse-train sampling technique, followed by the zero-order hold method. Impulse-train sampling involves the use of a periodic impulse train, which consists of a series of delta functions spaced at regular intervals determined by the sampling period. When a continuous-time signal is multiplied by this impulse train, it generates impulses with amplitudes corresponding to the signal's values at the sampling points.
In the...

Reconstruction of Signal using Interpolation

Reconstruction of Signal using Interpolation

Signal processing techniques are essential for accurately converting continuous signals to digital formats and vice versa. When a continuous signal is sampled with a period T, the resulting sampled signal exhibits replicas of the original spectrum in the frequency domain, spaced at intervals equal to the sampling frequency. To handle this sampled signal, a zero-order hold method can be applied, which creates a piecewise constant signal by retaining each sample's value until the next...

Sampling Plans

Sampling Plans

Sampling is a crucial step in analytical chemistry, allowing researchers to collect representative data from a large population. Common sampling methods include random, judgmental, systematic, stratified, and cluster sampling.
Random sampling is a method where each member of the population has an equal chance of being selected for the sample. It involves selecting individuals randomly, often using random number generators or lottery-type methods. For example, when analyzing the properties of a...

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The SPURS Algorithm for Resampling an Irregularly Sampled Signal onto a Cartesian Grid.

Amir Kiperwas, Daniel Rosenfeld, Yonina C Eldar

IEEE Transactions on Medical Imaging

|November 11, 2016

Summary

We developed SParse Uniform ReSampling (SPURS) to accurately convert non-Cartesian to Cartesian grid data. This efficient algorithm improves image reconstruction in MRI and other fields.

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Area of Science:

Signal Processing
Medical Imaging
Computational Science

Background:

Accurate data gridding is crucial for medical imaging (MRI, CT), radio astronomy, and geophysics.
Non-Cartesian sampling poses challenges for traditional Cartesian grid reconstruction methods.

Purpose of the Study:

To introduce SParse Uniform ReSampling (SPURS), an algorithm for efficient and accurate function resampling from non-Cartesian to Cartesian grids.
To demonstrate SPURS's effectiveness in Magnetic Resonance Imaging (MRI) data reconstruction.

Main Methods:

SPURS projects non-Cartesian samples onto a subspace defined by a kernel function, creating a sparse system of equations.
Efficient sparse solvers are used to determine signal coefficients, followed by projection using a digital linear shift invariant (LSI) filter.
The method can be iterated for enhanced reconstruction accuracy.

Main Results:

SPURS achieves low approximation error with low computational cost.
Simulations show SPURS outperforms existing reconstruction methods for MRI data.
Performance is robust across varying sampling densities, trajectories, and signal-to-noise ratios (SNR).

Conclusions:

SPURS offers a computationally efficient and accurate solution for non-Cartesian to Cartesian resampling.
The algorithm demonstrates significant advantages for MRI reconstruction from nonuniformly sampled k-space data.
SPURS has broad applicability in scientific fields requiring accurate gridding of sampled data.