Related papers: Learning-based Compressive Subsampling
The task of compressed sensing is to recover a sparse vector from a small number of linear and non-adaptive measurements, and the problem of finding a suitable measurement matrix is very important in this field. While most recent works…
Finding a suitable measurement matrix is an important topic in compressed sensing. Though the known random matrix, whose entries are drawn independently from a certain probability distribution, can be used as a measurement matrix and…
Random sampling in compressive sensing (CS) enables the compression of large amounts of input signals in an efficient manner, which is useful for many applications. CS reconstructs the compressed signals exactly with overwhelming…
Reconstructing continuous signals from a small number of discrete samples is a fundamental problem across science and engineering. In practice, we are often interested in signals with 'simple' Fourier structure, such as bandlimited,…
One-bit compressive sensing is concerned with the accurate recovery of an underlying sparse signal of interest from its one-bit noisy measurements. The conventional signal recovery approaches for this problem are mainly developed based on…
In this paper, we consider a compressed sensing problem of reconstructing a sparse signal from an undersampled set of noisy linear measurements. The regularized least squares or least absolute shrinkage and selection operator (LASSO)…
A combinatorial approach to compressive sensing based on a deterministic column replacement technique is proposed. Informally, it takes as input a pattern matrix and ingredient measurement matrices, and results in a larger measurement…
One of the major problems in modeling natural signals is that signals with very similar structure may locally have completely different measurements, e.g., images taken under different illumination conditions, or the speech signal captured…
Sampling is a fundamental aspect of any implementation of compressive sensing. Typically, the choice of sampling method is guided by the reconstruction basis. However, this approach can be problematic with respect to certain hardware…
A field known as Compressive Sensing (CS) has recently emerged to help address the growing challenges of capturing and processing high-dimensional signals and data sets. CS exploits the surprising fact that the information contained in a…
Compressed sensing is a signal processing method that acquires data directly in a compressed form. This allows one to make less measurements than what was considered necessary to record a signal, enabling faster or more precise measurement…
Compressive sampling offers a new paradigm for acquiring signals that are compressible with respect to an orthonormal basis. The major algorithmic challenge in compressive sampling is to approximate a compressible signal from noisy samples.…
We introduce a new class of measurement matrices for compressed sensing, using low order summaries over binary sequences of a given length. We prove recovery guarantees for three reconstruction algorithms using the proposed measurements,…
Traditional sampling theories consider the problem of reconstructing an unknown signal $x$ from a series of samples. A prevalent assumption which often guarantees recovery from the given measurements is that $x$ lies in a known subspace.…
In this paper, we consider the problem of recovering compressively sensed ultrasound images. We build on prior work, and consider a number of existing approaches that we consider to be the state-of-the-art. The methods we consider take…
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…
In applications ranging from communications to genetics, signals can be modeled as lying in a union of subspaces. Under this model, signal coefficients that lie in certain subspaces are active or inactive together. The potential subspaces…
A major challenge to implement the compressed sensing method for channel state information (CSI) acquisition lies in the design of a well-performed measurement matrix to reduce the dimension of sparse channel vectors. The widely adopted…
Parameterized mathematical models play a central role in understanding and design of complex information systems. However, they often cannot take into account the intricate interactions innate to such systems. On the contrary, purely…
This paper investigates the problem of recovering missing samples using methods based on sparse representation adapted especially for image signals. Instead of $l_2$-norm or Mean Square Error (MSE), a new perceptual quality measure is used…