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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...

Downsampling

Downsampling

When considering a sampled sequence with zero values between sampling instants, one can replace it by taking every N-th value of the sequence. At these integer multiples of N, the original and sampled sequences coincide. This process, known as decimation, involves extracting every N-th sample from a sequence, thereby creating a more efficient sequence.
The Fourier transform of the decimated sequence reveals a combination of scaled and shifted versions of the original spectrum. This...

Aliasing

Aliasing

Accurate signal sampling and reconstruction are crucial in various signal-processing applications. A time-domain signal's spectrum can be revealed using its Fourier transform. When this signal is sampled at a specific frequency, it results in multiple scaled replicas of the original spectrum in the frequency domain. The spacing of these replicas is determined by the sampling frequency.
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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.
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Computed Tomography

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Tomography refers to imaging by sections. Computed tomography (CT) is a non-invasive imaging technique that uses computers to analyze several cross-sectional X-rays to reveal minute details about structures in the body.
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Related Experiment Video

Updated: Apr 6, 2026

A Multimodal Wide-Field Fourier-Transform Raman Microscope

A Multimodal Wide-Field Fourier-Transform Raman Microscope

Published on: December 30, 2025

Compressive spectral imaging using variable number of measurements.

Yaohai Lin, Xuemei Xie, Guangming Shi

|July 21, 2015

Summary

This study introduces a novel spectral imaging method that reduces the number of sensors, not images, for practical applications. This approach utilizes coded dispersion and prior knowledge to acquire spectral images efficiently with variable measurements.

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Area of Science:

Optics and Photonics
Image Processing
Spectroscopy

Background:

Compressive spectral imaging typically reduces the number of acquired images.
Practical constraints like size, weight, and power limit sensor deployment in imaging systems.
Prior knowledge of scene objects can enhance spectral data acquisition.

Purpose of the Study:

To propose a novel spectral imaging method that minimizes the number of sensors on the imaging plane.
To address practical limitations in spectral imaging systems by reducing hardware requirements.
To leverage prior knowledge of scene objects for efficient spectral data acquisition.

Main Methods:

The proposed method employs coded dispersion to capture multiple spectral data points per sensor pixel.
It modifies the measurement matrix to allow for a variable number of measurements.
Prior knowledge about scene objects is integrated into the acquisition process.

Main Results:

Demonstrated the validity of the proposed method for spectral image acquisition.
Showed that the number of sensors can be significantly reduced.
Confirmed that spectral images can be acquired using a variable number of measurements when prior knowledge is available.

Conclusions:

The developed method offers a viable alternative to traditional compressive spectral imaging by reducing sensor count.
It effectively addresses hardware constraints by minimizing the number of required sensors.
The integration of prior knowledge and coded dispersion enables efficient spectral image acquisition with adjustable measurement parameters.