Related papers: On Variable Density Compressive Sampling
In this manuscript, we analyze the sparse signal recovery (compressive sensing) problem from the perspective of convex optimization by stochastic proximal gradient descent. This view allows us to significantly simplify the recovery analysis…
In many signal processing applications, one wishes to acquire images that are sparse in transform domains such as spatial finite differences or wavelets using frequency domain samples. For such applications, overwhelming empirical evidence…
Reducing acquisition time is a crucial challenge for many imaging techniques. Compressed Sensing (CS) theory offers an appealing framework to address this issue since it provides theoretical guarantees on the reconstruction of sparse…
Compressed Sensing refers to extracting a low-dimensional structured signal of interest from its incomplete random linear observations. A line of recent work has studied that, with the extra prior information about the signal, one can…
Recent results in compressed sensing showed that the optimal subsampling strategy should take into account the sparsity pattern of the signal at hand. This oracle-like knowledge, even though desirable, nevertheless remains elusive in most…
Non-convex constraints have recently proven a valuable tool in many optimisation problems. In particular sparsity constraints have had a significant impact on sampling theory, where they are used in Compressed Sensing and allow structured…
The structure of Magnetic Resonance Images (MRI) and especially their compressibility in an appropriate representation basis enables the application of the compressive sensing theory, which guarantees exact image recovery from incomplete…
Reducing acquisition time is of fundamental importance in various imaging modalities. The concept of variable density sampling provides a nice framework to achieve this. It was justified recently from a theoretical point of view in the…
In imaging modalities recording diffraction data, the original image can be reconstructed assuming known phases. When phases are unknown, oversampling and a constraint on the support region in the original object can be used to solve a…
Compressed sensing deals with the recovery of sparse signals from linear measurements. Without any additional information, it is possible to recover an $s$-sparse signal using $m \gtrsim s \log(d/s)$ measurements in a robust and stable way.…
The problem of minimization of the number of measurements needed for digital image acquisition and reconstruction with a given accuracy is addressed. Basics of the sampling theory are outlined to show that the lower bound of signal sampling…
In the area of near-field millimeter-wave imaging, the generalized sparse array synthesis (SAS) method is in great demand. The traditional methods usually employ the greedy algorithms, which may have the convergence problem. This paper…
This note complements the paper "The quest for optimal sampling: Computationally efficient, structure-exploiting measurements for compressed sensing" [2]. Its purpose is to present a proof of a result stated therein concerning the recovery…
Natural signals and images are well-known to be approximately sparse in transform domains such as Wavelets and DCT. This property has been heavily exploited in various applications in image processing and medical imaging. Compressed sensing…
The construction of highly incoherent frames, sequences of vectors placed on the unit hyper sphere of a finite dimensional Hilbert space with low correlation between them, has proven very difficult. Algorithms proposed in the past have…
Compressed sensing applied to magnetic resonance imaging (MRI) allows to reduce the scanning time by enabling images to be reconstructed from highly undersampled data. In this paper, we tackle the problem of designing a sampling mask for an…
Optimizing the acquisition matrix is useful for compressed sensing of signals that are sparse in overcomplete dictionaries, because the acquisition matrix can be adapted to the particular correlations of the dictionary atoms. In this paper…
In this effort, we propose a convex optimization approach based on weighted $\ell_1$-regularization for reconstructing objects of interest, such as signals or images, that are sparse or compressible in a wavelet basis. We recover the…
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…
We present the framework of slowly varying regression under sparsity, allowing sparse regression models to exhibit slow and sparse variations. The problem of parameter estimation is formulated as a mixed-integer optimization problem. We…