Related papers: Optimal Compressive Imaging of Fourier Data
There has been a growing interest in wideband spectrum sensing due to its applications in cognitive radios and electronic surveillance. To overcome the sampling rate bottleneck for wideband spectrum sensing, in this paper, we study the…
While the recent theory of compressed sensing provides an opportunity to overcome the Nyquist limit in recovering sparse signals, a solution approach usually takes a form of inverse problem of the unknown signal, which is crucially…
Inspired by the recently proposed Magnetic Resonance Fingerprinting (MRF) technique, we develop a principled compressed sensing framework for quantitative MRI. The three key components are: a random pulse excitation sequence following the…
Reconstruction of images from noisy linear measurements is a core problem in image processing, for which convex optimization methods based on total variation (TV) minimization have been the long-standing state-of-the-art. We present an…
The increasing demand for larger and higher fidelity simulations has made Adaptive Mesh Refinement (AMR) and unstructured mesh techniques essential to focus compute effort and memory cost on just the areas of interest in the simulation…
To accelerate MRI, the field of compressed sensing is traditionally concerned with optimizing the image quality after a partial undersampling of the measurable $\textit{k}$-space. In our work, we propose to change the focus from the quality…
Infinite-dimensional compressed sensing deals with the recovery of analog signals (functions) from linear measurements, often in the form of integral transforms such as the Fourier transform. This framework is well-suited to many real-world…
Compressed sensing provided a data-acquisition paradigm for sparse signals. Remarkably, it has been shown that practical algorithms provide robust recovery from noisy linear measurements acquired at a near optimal sampling rate. In many…
This paper presents modification of the TwIST algorithm for Compressive Sensing MRI images reconstruction. Compressive Sensing is new approach in signal processing whose basic idea is recovering signal form small set of available samples.…
Magnetic Resonance Imaging (MRI) is one of the fields that the compressed sensing theory is well utilized to reduce the scan time significantly leading to faster imaging or higher resolution images. It has been shown that a small fraction…
Compressed Sensing MRI reconstructs images of the body's internal anatomy from undersampled measurements, thereby reducing scan time. Recently, deep learning has shown great potential for reconstructing high-fidelity images from highly…
State-of-the-art methods for Convolutional Sparse Coding usually employ Fourier-domain solvers in order to speed up the convolution operators. However, this approach is not without shortcomings. For example, Fourier-domain representations…
We consider the problem of designing sparse sampling strategies for multidomain signals, which can be represented using tensors that admit a known multilinear decomposition. We leverage the multidomain structure of tensor signals and…
A compressed sensing method consists of a rectangular measurement matrix, $M \in \mathbbm{R}^{m \times N}$ with $m \ll N$, together with an associated recovery algorithm, $\mathcal{A}: \mathbbm{R}^m \rightarrow \mathbbm{R}^N$. Compressed…
Compressed sensing enables sparse sampling but relies on generic bases and random measurements, limiting efficiency and reconstruction quality. Optimal sensor placement uses historcal data to design tailored sampling patterns, yet its…
An intriguing phenomenon in many instances of compressed sensing is that the reconstruction quality is governed not just by the overall sparsity of the signal, but also on its structure. This paper is about understanding this phenomenon,…
Due to the many applications in Magnetic Resonance Imaging (MRI), Nuclear Magnetic Resonance (NMR), radio interferometry, helium atom scattering etc., the theory of compressed sensing with Fourier transform measurements has reached a mature…
In a series of recent papers (Adcock, Hansen and Poon, 2013, Appl. Comput. Harm. Anal. 45(5):3132-3167), (Adcock, Gataric and Hansen, 2014, SIAM J. Imaging Sci. 7(3):1690-1723) and (Adcock, Hansen, Kutyniok and Ma, 2015, SIAM J. Math. Anal.…
There is much recent interest in techniques to accelerate the data acquisition process in MRI by acquiring limited measurements. Often sophisticated reconstruction algorithms are deployed to maintain high image quality in such settings. In…
Fourier ptychography is a recently explored imaging method for overcoming the diffraction limit of conventional cameras with applications in microscopy and yielding high-resolution images. In order to splice together low-resolution images…