arXiv subjects

Y. C. Eldar

Publications and source records attributed to Y. C. Eldar.

5 recordsLinked to original sources

arXiv2012

Fourier Domain Beamforming for Medical Ultrasound

Sonography techniques use multiple transducer elements for tissue visualization. Signals detected at each element are sampled prior to digital beamforming. The required sampling rates are up to 4 times the Nyquist rate of the signal and result in considerable amount of data, that needs to be stored and processed. A developed technique, based on the finite rate of innovation model, compressed sensing (CS) and Xampling ideas, allows to reduce the number of samples needed to reconstruct an image comprised of strong reflectors. A significant drawback of this method is its inability to treat speckle, which is of significant importance in medical imaging. Here we build on previous work and show explicitly how to perform beamforming in the Fourier domain. Beamforming in frequency exploits the low bandwidth of the beamformed signal and allows to bypass the oversampling dictated by digital implementation of beamforming in time. We show that this allows to obtain the same beamformed image as in standard beamforming but from far fewer samples. Finally, we present an analysis based CS-technique that allows for further reduction in sampling rate, using only a portion of the beamformed signal's bandwidth, namely, sampling the signal at sub-Nyquist rates. We demonstrate our methods on in vivo cardiac ultrasound data and show that reductions up to 1/25 over standard beamforming rates are possible.

cs.IT↗

arXiv2011

Sparsity-based single-shot sub-wavelength coherent diffractive imaging

We present the experimental reconstruction of sub-wavelength features from the far-field intensity of sparse optical objects: sparsity-based sub-wavelength imaging combined with phase-retrieval. As examples, we demonstrate the recovery of random and ordered arrangements of 100 nm features with the resolution of 30 nm, with an illuminating wavelength of 532 nm. Our algorithmic technique relies on minimizing the number of degrees of freedom; it works in real-time, requires no scanning, and can be implemented in all existing microscopes - optical and non-optical.

physics.optics↗

arXiv2010

Far-Field Microscopy of Sparse Subwavelength Objects

We present the experimental reconstruction of sub-wavelength features from the far-field of sparse optical objects. We show that it is sufficient to know that the object is sparse, and only that, and recover 100 nm features with the resolution of 30 nm, for an illuminating wavelength of λ=532 nm. Our technique works in real-time, requires no scanning, and can be implemented in all existing microscopes - optical and non-optical.

physics.optics↗

arXiv2008

Beyond Bandlimited Sampling: Nonlinearities, Smoothness and Sparsity

Sampling theory has benefited from a surge of research in recent years, due in part to the intense research in wavelet theory and the connections made between the two fields. In this survey we present several extensions of the Shannon theorem, that have been developed primarily in the past two decades, which treat a wide class of input signals as well as nonideal sampling and nonlinear distortions. This framework is based on viewing sampling in a broader sense of projection onto appropriate subspaces, and then choosing the subspaces to yield interesting new possibilities. For example, our results can be used to uniformly sample non-bandlimited signals, and to perfectly compensate for nonlinear effects.

cs.IT↗

arXiv2001

Optimal Tight Frames and Quantum Measurement

Tight frames and rank-one quantum measurements are shown to be intimately related. In fact, the family of normalized tight frames for the space in which a quantum mechanical system lies is precisely the family of rank-one generalized quantum measurements (POVMs) on that space. Using this relationship, frame-theoretical analogues of various quantum-mechanical concepts and results are developed. The analogue of a least-squares quantum measurement is a tight frame that is closest in a least-squares sense to a given set of vectors. The least-squares tight frame is found for both the case in which the scaling of the frame is specified (constrained least-squares frame (CLSF)) and the case in which the scaling is free (unconstrained least-squares frame (ULSF)). The well-known canonical frame is shown to be proportional to the ULSF and to coincide with the CLSF with a certain scaling. Finally, the canonical frame vectors corresponding to a geometrically uniform vector set are shown to be geometrically uniform and to have the same symmetries as the original vector set.

quant-ph↗