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Recent breakthrough results in compressed sensing (CS) have established that many high dimensional objects can be accurately recovered from a relatively small number of non- adaptive linear projection observations, provided that the objects…
A new line of research uses compression methods to measure the similarity between signals. Two signals are considered similar if one can be compressed significantly when the information of the other is known. The existing compression-based…
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 this article, we introduce the concept of samplets by transferring the construction of Tausch-White wavelets to the realm of data. This way we obtain a multilevel representation of discrete data which directly enables data compression,…
This paper presents a tutorial for CS applications in communications networks. The Shannon's sampling theorem states that to recover a signal, the sampling rate must be as least the Nyquist rate. Compressed sensing (CS) is based on the…
We present improved sampling complexity bounds for stable and robust sparse recovery in compressed sensing. Our unified analysis based on l1 minimization encompasses the case where (i) the measurements are block-structured samples in order…
The compressive sensing (CS) scheme exploits much fewer measurements than suggested by the Nyquist-Shannon sampling theorem to accurately reconstruct images, which has attracted considerable attention in the computational imaging community.…
Compressed sensing aims at reconstructing sparse signals from significantly reduced number of samples, and a popular reconstruction approach is $\ell_1$-norm minimization. In this correspondence, a method called orthonormal expansion is…
Compressive sensing is a signal processing technique that enables the reconstruction of sparse signals from a limited number of measurements, leveraging the signal's inherent sparsity to facilitate efficient recovery. Recent works on the…
Compressed sensing (CS) is a promising approach to reduce the number of measurements in photoacoustic tomography (PAT) while preserving high spatial resolution. This allows to increase the measurement speed and to reduce system costs.…
Sparse decomposition has been widely used for different applications, such as source separation, image classification and image denoising. This paper presents a new algorithm for segmentation of an image into background and foreground text…
We propose to reduce the original well-posed problem of compressive sensing to weighted-MAX-SAT. Compressive sensing is a novel randomized data acquisition approach that linearly samples sparse or compressible signals at a rate much below…
This short note studies a variation of the Compressed Sensing paradigm introduced recently by Vaswani et al., i.e. the recovery of sparse signals from a certain number of linear measurements when the signal support is partially known. The…
Presented is a novel way to combine snapshot compressive imaging and lateral shearing interferometry in order to capture the spatio-spectral phase of an ultrashort laser pulse in a single shot. A deep unrolling algorithm is utilised for the…
The problem of recovering signals of high complexity from low quality sensing devices is analyzed via a combination of tools from signal processing and harmonic analysis. By using the rich structure offered by the recent development in…
Compressive sensing can overcome the Nyquist criterion and record images with a fraction of the usual number of measurements required. However, conventional measurement bases are susceptible to diffraction and scattering, prevalent in…
In compressed sensing (CS), sparse signals can be reconstructed from significantly fewer samples than required by the Nyquist-Shannon sampling theorem. While non-sparse signals can be sparsely represented in appropriate transformation…
In this work, we study the problem of reconstructing a sparse signal from a limited number of linear 'incoherent' noisy measurements, when a part of its support is known. The known part of the support may be available from prior knowledge…
The importance of regularization has been well established in image reconstruction -- which is the computational inversion of imaging forward model -- with applications including deconvolution for microscopy, tomographic reconstruction,…
Compressed sensing aims to undersample certain high-dimensional signals, yet accurately reconstruct them by exploiting signal characteristics. Accurate reconstruction is possible when the object to be recovered is sufficiently sparse in a…