Abstract: Certain aspects pertain to ptychographic imaging systems and methods with convex relaxation. In some aspects, a ptychographic imaging system with convex relaxation comprises one or more electromagnetic radiation sources, a digital radiation intensity detector, and a processor in communication with the digital radiation detector. The electromagnetic radiation provides coherent radiation to a specimen while the digital radiation intensity detector receives light transferred from the sample by diffractive optics and captures intensity distributions for a sequence of low resolution images having diversity. The processor generates a convex problem based on the sequence of low resolution images and optimizes the convex problem to reconstruct a high-resolution image of the specimen. In certain aspects, the convex problem is relaxed into a low-rank formulation.

Abstract: Certain aspects pertain to ptychographic imaging systems and methods with convex relaxation. In some aspects, a ptychographic imaging system with convex relaxation comprises one or more electromagnetic radiation sources, a digital radiation intensity detector, and a processor in communication with the digital radiation detector. The electromagnetic radiation provides coherent radiation to a specimen while the digital radiation intensity detector receives light transferred from the sample by diffractive optics and captures intensity distributions for a sequence of low resolution images having diversity. The processor generates a convex problem based on the sequence of low resolution images and optimizes the convex problem to reconstruct a high-resolution image of the specimen. In certain aspects, the convex problem is relaxed into a low-rank formulation.

Abstract: Certain aspects pertain to ptychographic imaging systems and methods with convex relaxation. In some aspects, a ptychographic imaging system with convex relaxation comprises one or more electromagnetic radiation sources, a digital radiation intensity detector, and a processor in communication with the digital radiation detector. The electromagnetic radiation provides coherent radiation to a specimen while the digital radiation intensity detector receives light transferred from the sample by diffractive optics and captures intensity distributions for a sequence of low resolution images having diversity. The processor generates a convex problem based on the sequence of low resolution images and optimizes the convex problem to reconstruct a high-resolution image of the specimen. In certain aspects, the convex problem is relaxed into a low-rank formulation.

Abstract: A typical data acquisition system takes periodic samples of a signal, image, or other data, often at the so-called Nyquist/Shannon sampling rate of two times the data bandwidth in order to ensure that no information is lost. In applications involving wideband signals, the Nyquist/Shannon sampling rate is very high, even though the signals may have a simple underlying structure. Recent developments in mathematics and signal processing have uncovered a solution to this Nyquist/Shannon sampling rate bottlenck for signals that are sparse or compressible in some representation. We demonstrate and reduce to practice methods to extract information directly from an analog or digital signal based on altering our notion of sampling to replace uniform time samples with more general linear functionals. One embodiment of our invention is a low-rate analog-to-information converter that can replace the high-rate analog-to-digital converter in certain applications involving wideband signals.

Abstract: A typical data acquisition system takes periodic samples of a signal, image, or other data, often at the so-called Nyquist/Shannon sampling rate of two times the data bandwidth in order to ensure that no information is lost. In applications involving wideband signals, the Nyquist/Shannon sampling rate is very high, even though the signals may have a simple underlying structure. Recent developments in mathematics and signal processing have uncovered a solution to this Nyquist/Shannon sampling rate bottlenck for signals that are sparse or compressible in some representation. We demonstrate and reduce to practice methods to extract information directly from an analog or digital signal based on altering our notion of sampling to replace uniform time samples with more general linear functionals. One embodiment of our invention is a low-rate analog-to-information converter that can replace the high-rate analog-to-digital converter in certain applications involving wideband signals.