Related papers: Uncertainty Relations for Shift-Invariant Analog S…
Despite strong empirical performance for image classification, deep neural networks are often regarded as ``black boxes'' and they are difficult to interpret. On the other hand, sparse convolutional models, which assume that a signal can be…
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…
Optimal sensor placement is a central challenge in the design, prediction, estimation, and control of high-dimensional systems. High-dimensional states can often leverage a latent low-dimensional representation, and this inherent…
The problem of super-resolution is concerned with the reconstruction of temporally/spatially localized events (or spikes) from samples of their convolution with a low-pass filter. Distinct from prior works which exploit sparsity in…
The promise of compressive sensing (CS) has been offset by two significant challenges. First, real-world data is not exactly sparse in a fixed basis. Second, current high-performance recovery algorithms are slow to converge, which limits CS…
We consider the problem of subspace estimation in situations where the number of available snapshots and the observation dimension are comparable in magnitude. In this context, traditional subspace methods tend to fail because the…
Compressed sensing is a relatively new mathematical paradigm that shows a small number of linear measurements are enough to efficiently reconstruct a large dimensional signal under the assumption the signal is sparse. Applications for this…
The theory behind compressive sampling pre-supposes that a given sequence of observations may be exactly represented by a linear combination of a small number of basis vectors. In practice, however, even small deviations from an exact…
A fundamental problem faced by object recognition systems is that objects and their features can appear in different locations, scales and orientations. Current deep learning methods attempt to achieve invariance to local translations via…
Over the past years, there are increasing interests in recovering the signals from undersampling data where such signals are sparse under some orthogonal dictionary or tight framework, which is referred to be sparse synthetic model. More…
We present a novel approach for recovering a sparse signal from cross-correlated data. Cross-correlations naturally arise in many fields of imaging, such as optics, holography and seismic interferometry. Compared to the sparse signal…
Understanding 3D object shapes necessitates shape representation by object parts abstracted from results of instance and semantic segmentation. Promising shape representations enable computers to interpret a shape with meaningful parts and…
We survey a new paradigm in signal processing known as "compressive sensing". Contrary to old practices of data acquisition and reconstruction based on the Shannon-Nyquist sampling principle, the new theory shows that it is possible to…
Many natural signals exhibit a sparse representation, whenever a suitable describing model is given. Here, a linear generative model is considered, where many sparsity-based signal processing techniques rely on such a simplified model. As…
In the dictionary learning (or sparse coding) problem, we are given a collection of signals (vectors in $\mathbb{R}^d$), and the goal is to find a "basis" in which the signals have a sparse (approximate) representation. The problem has…
Atomic norm minimization is a convex optimization framework to recover point sources from a subset of their low-pass observations, or equivalently the underlying frequencies of a spectrally-sparse signal. When the amplitudes of the sources…
We investigate the use of sparse coding and dictionary learning in the context of multitask and transfer learning. The central assumption of our learning method is that the tasks parameters are well approximated by sparse linear…
The problem of sparse multichannel blind deconvolution (S-MBD) arises frequently in many engineering applications such as radar/sonar/ultrasound imaging. To reduce its computational and implementation cost, we propose a compression method…
In linear inverse problems, the goal is to recover a target signal from undersampled, incomplete or noisy linear measurements. Typically, the recovery relies on complex numerical optimization methods; recent approaches perform an unfolding…
Recently, great attention was intended toward overcomplete dictionaries and the sparse representations they can provide. In a wide variety of signal processing problems, sparsity serves a crucial property leading to high performance.…