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We propose and demonstrate, numerically and experimentally, use of sparsity as prior information for extending the capabilities and performance of techniques and devices for laser pulse diagnostics. We apply the concept of sparsity in three different applications. First, we improve a photodiode-oscilloscope system's resolution for measuring the intensity structure of laser pulses. Second, we demonstrate the intensity profile reconstruction of ultrashort laser pulses from intensity autocorrelation measurements. Finally, we use a sparse representation of pulses (amplitudes and phases) to retrieve measured pulses from incomplete spectrograms of cross-correlation frequency-resolved optical gating traces.

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Undersampling of functional MRI (fMRI) data leads to increased temporal resolution, as it allows shorter acquisition time per frame. High quality reconstruction of fMRI data from undersampled measurements requires proper modeling of the fMRI data. Recent publications suggest that the fMRI signal is a superposition of periodic and aperiodic signals. In this paper we develop an fMRI reconstruction approach based on this modeling. The fMRI data is assumed to be composed of two components: a component that holds a sum of periodic signals which is sparse in the temporal Fourier domain and an component that holds the remaining imaging information (consisting of the background and aperiodic signals) which has low rank. Data reconstruction is done by solving a constrained problem that enforces a fixed, moderate rank on one of the components, and a limited number of temporal frequencies on the other. Our approach is coined PEAR - PEriodic and ApeRiodic signal separation for fast fMRI. Experimental results are based on fMRI reconstruction using realistic timecourses. Evaluation was performed both quantitatively and visually versus ground truth. Results demonstrate PEAR's improvement in estimating the realistic timecourses versus state-of-the-art approaches at acceleration ratio of R=16.6.

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In many clinical MRI scenarios, existing imaging information can be used to significantly shorten acquisition time or improve Signal to Noise Ratio (SNR). In those cases, a previously acquired image can serve as a reference image, that may exhibit similarity in some sense to the image being acquired. Examples include similarity between adjacent slices in high resolution MRI, similarity between various contrasts in the same scans and similarity between different scans of the same patients. In this paper we present a general framework for utilizing reference images for fast MRI. We take into account that the reference image may exhibit low similarity with the acquired image and develop a hybrid adaptive-weighted approach for sampling and reconstruction. Experiments demonstrate the performance of the method in three different clinical MRI scenarios: SNR improvement in high resolution brain MRI, utilizing similarity between T2-weighted and fluid-attenuated inversion recovery (FLAIR) for fast FLAIR scanning and utilizing similarity between baseline and follow-up scans for fast follow-up scanning.

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Coherent Diffractive Imaging (CDI) is an algorithmic imaging technique where intricate features are reconstructed from measurements of the freely diffracting intensity pattern. An important goal of such lensless imaging methods is to study the structure of molecules that cannot be crystallized. Ideally, one would want to perform CDI at the highest achievable spatial resolution and in a single-shot measurement such that it could be applied to imaging of ultrafast events. However, the resolution of current CDI techniques is limited by the diffraction limit, hence they cannot resolve features smaller than one half the wavelength of the illuminating light. Here, we present sparsity-based single-shot subwavelength resolution CDI: algorithmic reconstruction of subwavelength features from far-field intensity patterns, at a resolution several times better than the diffraction limit. This work paves the way for subwavelength CDI at ultrafast rates, and it can considerably improve the CDI resolution with X-ray free-electron lasers and high harmonics.

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