Pulse shape design using iterative projections

In this paper, the pulse shape design for various communication systems including PAM, FSK, and PSK is considered. The pulse is designed by imposing constraints on the time and frequency domains constraints on the autocorrelation function of the pulse shape. Intersymbol interference, finite duration and spectral mask restrictions are a few examples leading to convex sets in L 2. The autocorrelation function of the pulse is obtained by performing iterative projections onto convex sets. After this step, the minimum phase or maximum phase pulse producing the autocorrelation function is obtained by cepstral deconvolution

Signal recovery from partial fractional fourier domain information and pulse shape design using iterative projections

Cataloged from PDF version of article.Signal design and recovery problems come up in a wide variety of applications in signal processing. In this thesis, we first investigate the problem of pulse shape design for use in communication settings with matched filtering where the rate of communication, intersymbol interference, and bandwidth of the signal constitute conflicting themes. In order to design pulse shapes that satisfy certain criteria such as bit rate, spectral characteristics, and worst case degradation due to intersymbol interference, we benefit from the wellknown Projections Onto Convex Sets. Secondly, we investigate the problem of signal recovery from partial information in fractional Fourier domains. Fractional Fourier transform is a mathematical generalization of the ordinary Fourier transform, the latter being a special case of the first. Here, we assume that low resolution or partial information in different fractional Fourier transform domains is available in different intervals. These information intervals define convex sets and can be combined within the Projections Onto Convex Sets framework. We present generic scenarios and simulation examples in order to illustrate the use of the method.Güven, H EmreM.S

Quick X-ray microtomography using a laser-driven betatron source

Laser-driven X-ray sources are an emerging alternative to conventional X-ray tubes and synchrotron sources. We present results on microtomographic X-ray imaging of a cancellous human bone sample using synchrotron-like betatron radiation. The source is driven by a 100-TW-class titanium-sapphire laser system and delivers over $10^8$ X-ray photons per second. Compared to earlier studies, the acquisition time for an entire tomographic dataset has been reduced by more than an order of magnitude. Additionally, the reconstruction quality benefits from the use of statistical iterative reconstruction techniques. Depending on the desired resolution, tomographies are thereby acquired within minutes, which is an important milestone towards real-life applications of laser-plasma X-ray sources

Sampling and Recovery of Pulse Streams

Compressive Sensing (CS) is a new technique for the efficient acquisition of signals, images, and other data that have a sparse representation in some basis, frame, or dictionary. By sparse we mean that the N-dimensional basis representation has just K<<N significant coefficients; in this case, the CS theory maintains that just M = K log N random linear signal measurements will both preserve all of the signal information and enable robust signal reconstruction in polynomial time. In this paper, we extend the CS theory to pulse stream data, which correspond to S-sparse signals/images that are convolved with an unknown F-sparse pulse shape. Ignoring their convolutional structure, a pulse stream signal is K=SF sparse. Such signals figure prominently in a number of applications, from neuroscience to astronomy. Our specific contributions are threefold. First, we propose a pulse stream signal model and show that it is equivalent to an infinite union of subspaces. Second, we derive a lower bound on the number of measurements M required to preserve the essential information present in pulse streams. The bound is linear in the total number of degrees of freedom S + F, which is significantly smaller than the naive bound based on the total signal sparsity K=SF. Third, we develop an efficient signal recovery algorithm that infers both the shape of the impulse response as well as the locations and amplitudes of the pulses. The algorithm alternatively estimates the pulse locations and the pulse shape in a manner reminiscent of classical deconvolution algorithms. Numerical experiments on synthetic and real data demonstrate the advantages of our approach over standard CS

Coherent X-ray Diffractive Imaging; applications and limitations

The inversion of a diffraction pattern offers aberration-free diffraction-limited 3D images without the resolution and depth-of-field limitations of lens-based tomographic systems, the only limitation being radiation damage. We review our experimental results, discuss the fundamental limits of this technique and future plans.Comment: 7 pages, 8 figure