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Deep De-Aliasing for Fast Compressive Sensing MRI
Get PDFFast Magnetic Resonance Imaging (MRI) is highly in demand for many clinical applications in order to reduce the scanning cost and improve the patient experience. This can also potentially increase the image quality by reducing the motion artefacts and contrast washout. However, once an image field of view and the desired resolution are chosen, the minimum scanning time is normally determined by the requirement of acquiring sufficient raw data to meet the Nyquist-Shannon sampling criteria. Compressive Sensing (CS) theory has been perfectly matched to the MRI scanning sequence design with much less required raw data for the image reconstruction. Inspired by recent advances in deep learning for solving various inverse problems, we propose a conditional Generative Adversarial Networks-based deep learning framework for de-aliasing and reconstructing MRI images from highly undersampled data with great promise to accelerate the data acquisition process. By coupling an innovative content loss with the adversarial loss our de-aliasing results are more realistic. Furthermore, we propose a refinement learning procedure for training the generator network, which can stabilise the training with fast convergence and less parameter tuning. We demonstrate that the proposed framework outperforms state-of-the-art CS-MRI methods, in terms of reconstruction error and perceptual image quality. In addition, our method can reconstruct each image in 0.22ms--0.37ms, which is promising for real-time applications
Moment inversion problem for piecewise D-finite functions
Full text linkWe consider the problem of exact reconstruction of univariate functions with
jump discontinuities at unknown positions from their moments. These functions
are assumed to satisfy an a priori unknown linear homogeneous differential
equation with polynomial coefficients on each continuity interval. Therefore,
they may be specified by a finite amount of information. This reconstruction
problem has practical importance in Signal Processing and other applications.
It is somewhat of a ``folklore'' that the sequence of the moments of such
``piecewise D-finite''functions satisfies a linear recurrence relation of
bounded order and degree. We derive this recurrence relation explicitly. It
turns out that the coefficients of the differential operator which annihilates
every piece of the function, as well as the locations of the discontinuities,
appear in this recurrence in a precisely controlled manner. This leads to the
formulation of a generic algorithm for reconstructing a piecewise D-finite
function from its moments. We investigate the conditions for solvability of the
resulting linear systems in the general case, as well as analyze a few
particular examples. We provide results of numerical simulations for several
types of signals, which test the sensitivity of the proposed algorithm to
noise
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