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Structured compressed sensing: From theory to applications
 IEEE TRANS. SIGNAL PROCESS
, 2011
"... Compressed sensing (CS) is an emerging field that has attracted considerable research interest over the past few years. Previous review articles in CS limit their scope to standard discretetodiscrete measurement architectures using matrices of randomized nature and signal models based on standard ..."
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Cited by 104 (16 self)
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Compressed sensing (CS) is an emerging field that has attracted considerable research interest over the past few years. Previous review articles in CS limit their scope to standard discretetodiscrete measurement architectures using matrices of randomized nature and signal models based on standard sparsity. In recent years, CS has worked its way into several new application areas. This, in turn, necessitates a fresh look on many of the basics of CS. The random matrix measurement operator must be replaced by more structured sensing architectures that correspond to the characteristics of feasible acquisition hardware. The standard sparsity prior has to be extended to include a much richer class of signals and to encode broader data models, including continuoustime signals. In our overview, the theme is exploiting signal and measurement structure in compressive sensing. The prime focus is bridging theory and practice; that is, to pinpoint the potential of structured CS strategies to emerge from the math to the hardware. Our summary highlights new directions as well as relations to more traditional CS, with the hope of serving both as a review to practitioners wanting to join this emerging field, and as a reference for researchers that attempts to put some of the existing ideas in perspective of practical applications.
Stolt's fk migration for plane wave ultrasound imaging
 IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control
, 2013
"... Abstract—Ultrafast ultrasound is an emerging modality that offers new perspectives and opportunities in medical imaging. Plane wave imaging (PWI) allows one to attain very high frame rates by transmission of planar ultrasound wavefronts. As a plane wave reaches a given scatterer, the latter become ..."
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Abstract—Ultrafast ultrasound is an emerging modality that offers new perspectives and opportunities in medical imaging. Plane wave imaging (PWI) allows one to attain very high frame rates by transmission of planar ultrasound wavefronts. As a plane wave reaches a given scatterer, the latter becomes a secondary source emitting upward spherical waves and creating a diffraction hyperbola in the received RF signals. To produce an image of the scatterers, all the hyperbolas must be migrated back to their apexes. To perform beamforming of plane wave echo RFs and return highquality images at high frame rates, we propose a new migration method carried out in the frequencywavenumber (fk) domain. The fk migration for PWI has been adapted from the Stolt migration for seismic imaging. This migration technique is based on the exploding reflector model (ERM), which consists in assuming that all the scatterers explode in concert and become acoustic sources. The classical ERM model, however, is not appropriate for PWI. We showed that the ERM can be made suitable for PWI by a spatial transformation of the hyperbolic traces present in the RF data. In vitro experiments were performed to outline the advantages of PWI with Stolt’s fk migration over the conventional delayandsum (DAS) approach. The Stolt’s fk migration was also compared with the Fourierbased method developed by J.Y. Lu. Our findings show that multiangle compounded fk migrated images are of quality similar to those obtained with a stateoftheart dynamic focusing mode. This remained true even with a very small number of steering angles, thus ensuring a highly competitive frame rate. In addition, the new FFTbased fk migration provides comparable or better contrasttonoise ratio and lateral resolution than the Lu’s and DAS migration schemes. Matlab codes for the Stolt’s fk migration for PWI are provided. I.
2Université de Toulouse, IRIT
"... Abstract — One of the fundamental theorem in information theory is the socalled sampling theorem also known as ShannonNyquist theorem. This theorem aims at giving the minimal frequency needed to sample and reconstruct perfectly an analog bandlimited signal. Compressive sensing (or compressed sens ..."
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Abstract — One of the fundamental theorem in information theory is the socalled sampling theorem also known as ShannonNyquist theorem. This theorem aims at giving the minimal frequency needed to sample and reconstruct perfectly an analog bandlimited signal. Compressive sensing (or compressed sensing, compressive sampling) or CS in short is a recent theory that allows, if the signal to be reconstructed satisfies a number of conditions, to decrease the amount of data needed to reconstruct the signal. As a result this theory can be used for at least two purposes: i) accelerate the acquisition rate without decreasing the reconstructed signal quality (e.g. in terms of resolution, SNR, contrast …) ii) improve the image quality without increasing the quantity of needed data. Even if medical ultrasound is a domain where several potential applications can be highlighted, the use of this theory in this domain is extremely recent. In this paper we review the basic theory of compressive sensing. Then, a review of the existing CS studies in the field of medical ultrasound is given: reconstruction of sparse scattering maps, prebeamforming channel data, postbeamforming signals and slow time Doppler data. Finally the open problems and challenges to be tackled in order to make the application of CS to medical US a reality will be given.