How does compressed sensing work?

Compressed sensing takes advantage of the redundancy in many interesting signals—they are not pure noise. Compressed sensing typically starts with taking a weighted linear combination of samples also called compressive measurements in a basis different from the basis in which the signal is known to be sparse.

What is compressed sensing in image processing?

Compressed sensing (CS) is an image acquisition method, where only few random measurements are taken instead of taking all the necessary samples as suggested by Nyquist sampling theorem. It is one of the most active research areas in the past decade.

Who invented compressive sensing?

Donoho
2 Background. Although the term compressed sensing (compressive sensing) was coined only recently with the paper by Donoho [47], followed by a huge research activity, such a development did not start out of thin air.

What is compressed sensing in MRI?

Compressed sensing (CS) is a method for accelerating MRI acquisition by acquiring less data through undersampling of k-space. This has the potential to mitigate the time-intensiveness of MRI. Studies have successfully accelerated MRI with this technology, with varying degrees of success.

What is sensing matrix?

One of the most important aspects of compressed sensing (CS) theory is an efficient design of sensing matrices. These sensing matrices are accountable for the required signal compression at the encoder end and its exact or approximate reconstruction at the decoder end.

What is signal sparsity?

A signal is said to be sparse if it can be represented in a basis or frame (e.g Fourier, Wavelets, Curvelets, etc.) in which the curve obtained by plotting the obtained coefficients, sorted by their decreasing absolute values, exhibits a polynomial decay.

What is deep compressed sensing?

Yan Wu, Mihaela Rosca, Timothy Lillicrap. Compressed sensing (CS) provides an elegant framework for recovering sparse signals from compressed measurements. For example, CS can exploit the structure of natural images and recover an image from only a few random measurements.

What is a sensing matrix?

What is compress sense?

Compressed sensing is a signal processing technique built on the fact that signals contain redundant information. In MR this technique is used to reconstruct a full image from severely under-sampled data (in k-space) while maintaining virtually equivalent image quality.

Why is k-space called k-space?

The k-space is an extension of the concept of Fourier space well known in MR imaging. The k-space represents the spatial frequency information in two or three dimensions of an object. The k-space is defined by the space covered by the phase and frequency encoding data.

What is incoherence in compressed sensing?

The CS theory asserts that one can recover certain signals and images from far fewer samples or measurements than traditional methods use. Put differently, incoherence says that unlike the signal of interest, the sampling/sensing waveforms have an extremely dense representation in Ψ.

What is orthogonal matching pursuit?

Abstract: We consider the orthogonal matching pursuit (OMP) algorithm for the recovery of a high-dimensional sparse signal based on a small number of noisy linear measurements. OMP is an iterative greedy algorithm that selects at each step the column, which is most correlated with the current residuals.

What is compressive sensing?

Recently, compressive sensing or compressed sensing (will be referred as CS henceforth) has been an active research area in the field of signal processing and communication. It has been applied to Wireless sensor networks, video processing and image processing and up to some extent on speech signal processing also.

What is the best Fourier transform for compressed sensing?

In compressed sensing, we undersample the measurements. Recall that compressed sensing requires an incoherent measurement matrix. One good choice is the undersampled Fourier transform.

Why is the recovery stage of compressed sensing the most challenging?

The recovery stage of compressed sensing is the most challenging because it requires significant a priori knowledge of the signal. For our test signal, we can reconstruct the original signal fully by taking the two largest Fourier coefficients and renormalizing the signal energy.

Is compressed sensing a disruptive innovation in seismic acquisition?

Compressed sensing has the potential to be a disruptive innovation in seismic acquisition, and it poses an interesting high-risk, high-reward engineering problem. Bryan, K., and T. Leise, 2013, Making do with less: An introduction to compressed sensing: SIAM Review, 55, no. 3, 547–566, http://dx.doi.org/10.1137/110837681.