Related papers: Optimally Sparse Frames
Finite unit norm tight frames provide Parseval-like decompositions of vectors in terms of redundant components of equal weight. They are known to be exceptionally robust against additive noise and erasures, and as such, have great potential…
As conventional frame-based cameras suffer from high energy consumption and latency, several new types of image sensors have been devised, with some of them exploiting the sparsity of natural images in some transform domains. Instead of…
We introduce a class of finite tight frames called prime tight frames and prove some of their elementary properties. In particular, we show that any finite tight frame can be written as a union of prime tight frames. We then characterize…
We consider the problem of sparse atomic optimization, where the notion of "sparsity" is generalized to meaning some linear combination of few atoms. The definition of atomic set is very broad; popular examples include the standard basis,…
In compressed sensing one measures sparse signals directly in a compressed form via a linear transform and then reconstructs the original signal. However, it is often the case that the linear transform itself is known only approximately, a…
Most rational systems can be described in terms of orthonormal basis functions. This paper considers the reconstruction of a sparse coefficient vector for a rational transfer function under a pair of orthonormal rational function bases and…
We consider a minimization problem whose objective function is the sum of a fidelity term, not necessarily convex, and a regularization term defined by a positive regularization parameter $\lambda$ multiple of the $\ell_0$ norm composed…
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…
Hilbert space frames generalize orthonormal bases to allow redundancy in representations of vectors while keeping good reconstruction properties. A frame comes with an associated frame operator encoding essential properties of the frame. We…
Sparse depth measurements are widely available in many applications such as augmented reality, visual inertial odometry and robots equipped with low cost depth sensors. Although such sparse depth samples work well for certain applications…
Conventional lens-based imaging techniques have long been limited to capturing only the intensity distribution of objects, resulting in the loss of other crucial dimensions such as spectral data. Here, we report a spectral lens that…
The problem of how to find a sparse representation of a signal is an important one in applied and computational harmonic analysis. It is closely related to the problem of how to reconstruct a sparse vector from its projection in a much…
It is now well understood that (1) it is possible to reconstruct sparse signals exactly from what appear to be highly incomplete sets of linear measurements and (2) that this can be done by constrained L1 minimization. In this paper, we…
The choice of the sensing matrix is crucial in compressed sensing. Random Gaussian sensing matrices satisfy the restricted isometry property, which is crucial for solving the sparse recovery problem using convex optimization techniques.…
Imaging spectrometers measure electromagnetic energy scattered in their instantaneous field view in hundreds or thousands of spectral channels with higher spectral resolution than multispectral cameras. Imaging spectrometers are therefore…
Spectral functions of large matrices contains important structural information about the underlying data, and is thus becoming increasingly important. Many times, large matrices representing real-world data are \emph{sparse} or \emph{doubly…
Optimal extraction is a key step in processing the raw images of spectra as registered by two-dimensional detector arrays to a one-dimensional format. Previously reported algorithms reconstruct models for a mean one-dimensional spatial…
Structured sparse optimization is an important and challenging problem for analyzing high-dimensional data in a variety of applications such as bioinformatics, medical imaging, social networks, and astronomy. Although a number of structured…
Human visual recognition is a sparse process, where only a few salient visual cues are attended to rather than traversing every detail uniformly. However, most current vision networks follow a dense paradigm, processing every single visual…
In recent years, a large amount of multi-disciplinary research has been conducted on sparse models and their applications. In statistics and machine learning, the sparsity principle is used to perform model selection---that is,…