Compressed Sensing

Definition of Compressed Sensing

Compressed sensing is a signal processing technique used in data acquisition and reconstruction, where fewer samples are collected than traditionally required by the Nyquist-Shannon sampling theorem. It exploits the sparsity of the signal in a transform domain and utilizes optimization algorithms for accurate reconstruction. This approach significantly reduces the amount of data needed and enables efficient data storage and processing while maintaining the integrity of the original signal.


The phonetics of the keyword “Compressed Sensing” can be represented in the International Phonetic Alphabet (IPA) as /kəmˈprɛst ˈsɛnsɪŋ/.

Key Takeaways

  1. Compressed Sensing is a signal processing and acquisition technique that enables the reconstruction of a signal using relatively few samples, significantly reducing the number of measurements required compared to the traditional Nyquist-Shannon sampling theorem.
  2. This technique exploits the sparsity of a signal, meaning that its essential information content can be captured in fewer measurements, provided that the signal has a compressible or sparse representation in some known basis.
  3. Compressed Sensing has various practical applications, such as medical imaging, radar systems, and communications, and it is especially beneficial in scenarios where acquiring large amounts of data is challenging, time-consuming, or expensive.

Importance of Compressed Sensing

Compressed sensing is a significant technology term because it enables efficient data acquisition and reconstruction with fewer measurements, particularly useful in fields like signal processing, imaging, and data compression.

By exploiting the inherent sparsity of many real-world signals, compressed sensing optimizes the sampling process, reducing the overall time and resources needed for data acquisition.

Consequently, this technological advancement contributes to increased performance in various applications, such as medical imaging, remote sensing, and communication systems.

Ultimately, compressed sensing allows for more efficient data management, improved processing speeds, lower storage requirements, and, in certain cases, reduced energy consumption, making it an essential term and technique in modern technology.


Compressed sensing, or compressive sensing, serves the purpose of revolutionizing the way we gather and process information in various fields, such as image and signal processing, medical imaging, and remote sensing. This innovative technique allows for the effective reconstruction of sparse signals from a small number of measurements, which results in quicker data acquisition and reduced storage requirements.

The core idea behind compressed sensing is that it can recover a signal that is sparse in some domain by taking far fewer samples than suggested by the traditional Nyquist-Shannon sampling theorem, which is the foundation of digital signal processing. The widespread use of compressed sensing can be observed in applications such as MRI scans, where rapid data acquisition leads to reduced scanning time and increased patient comfort, as well as in the field of geophysics where it assists in reducing the number of required observations during seismic surveying.

Furthermore, by leveraging its abilities in compressing massive amounts of data, this groundbreaking technique can save significant bandwidth, storage, and energy consumption in communication systems. Overall, compressed sensing has unlocked new possibilities across multiple disciplines by offering a more efficient approach to managing data-heavy tasks.

Examples of Compressed Sensing

Compressed Sensing (CS) is a signal processing technique that allows for the acquisition and reconstruction of sparse signals using fewer samples than traditionally required by the Nyquist-Shannon sampling theorem. Here are three real-world examples of how Compressed Sensing is used in technology:

Medical Imaging (MRI): Compressed Sensing has been successfully applied to Magnetic Resonance Imaging (MRI) to shorten the scanning time and minimize patient discomfort without sacrificing image quality. By utilizing the sparsity of the signals in MRI, CS techniques enable the acquisition of fewer samples, allowing for faster image reconstruction, reduced patient discomfort, and increased throughput for medical professionals.

Seismic Exploration: In the oil and gas industry, Compressed Sensing has been applied to increase the efficiency of seismic data acquisition. Traditional seismic exploration requires a large number of sensors and a high density of sampling points, leading to high costs and significant amounts of data to process. Using Compressed Sensing algorithms, sparse data can be acquired and reconstructed, reducing the number of sensors, the amount of data to process, and ultimately lowering costs while maintaining the quality of seismic images.

Wireless Sensor Networks: Compressed Sensing can be utilized in wireless sensor networks for data acquisition and transmission. In some applications, such as environmental monitoring, a large number of sensors are deployed to collect data from a broad area. Since the sensed data often exhibit sparse characteristics, CS can be applied to minimize the amount of data transmitted, thereby reducing energy consumption, prolonging the network’s lifetime, and reducing the complexity of data processing.

FAQ: Compressed Sensing

What is Compressed Sensing?

Compressed Sensing is a signal processing technique that allows efficient acquisition and reconstruction of sparse signals using fewer samples than traditional methods. It leverages the sparsity of a signal to recover it from limited or incomplete measurements.

How does Compressed Sensing work?

Compressed Sensing works by exploiting the sparsity of a signal in a specific basis or representation. It uses linear projections to take random measurements from the signal and applies optimization algorithms to recover the original signal from these measurements. The result is a robust and efficient reconstruction process that requires less sampling than traditional methods.

What are the applications of Compressed Sensing?

Compressed Sensing has applications in various fields, including imaging, signal processing, telecommunications, and machine learning. Some specific examples are magnetic resonance imaging (MRI), radar imaging, wireless sensor networks, data compression, and feature extraction in machine learning.

What are the requirements for Compressed Sensing to work?

For Compressed Sensing to be effective, the signal must be sparse or compressible in a known basis or representation. Additionally, the sensing matrix used for linear projections must satisfy certain properties, such as incoherence and the Restricted Isometry Property (RIP). Lastly, an appropriate optimization algorithm, like Basis Pursuit or Orthogonal Matching Pursuit, must be employed to recover the original signal.

What are the benefits of Compressed Sensing?

Compressed Sensing provides several benefits, including faster data acquisition, reduced storage requirements, and the ability to recover signals with minimal loss of information. As a result, it is an essential tool for applications where traditional methods are inefficient, slow, or impractical.

Related Technology Terms

  • Signal Sparsity
  • Reconstruction Algorithms
  • Measurement Matrices
  • Sampling Theory
  • Orthogonal Matching Pursuit

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