Related papers: Gabor fusion frames generated by difference sets
This paper considers a general framework for massive random access based on sparse superposition coding. We provide guidelines for the code design and propose the use of constant-weight codes in combination with a dictionary design based on…
Sparse recovery is one of the most fundamental and well-studied inverse problems. Standard statistical formulations of the problem are provably solved by general convex programming techniques and more practical, fast (nearly-linear time)…
In this paper we characterize and construct novel oversampled filter banks implementing fusion frames. A fusion frame is a sequence of orthogonal projection operators whose sum can be inverted in a numerically stable way. When properly…
In this paper a sublinear time algorithm is presented for the reconstruction of functions that can be represented by just few out of a potentially large candidate set of Fourier basis functions in high spatial dimensions, a so-called…
We perform a time-frequency analysis of Fourier multipliers and, more generally, pseudodifferential operators with symbols of Gevrey, analytic and ultra-analytic regularity. As an application we show that Gabor frames, which provide…
Gabor analysis is one of the most common instances of time-frequency signal analysis. Choosing a suitable window for the Gabor transform of a signal is often a challenge for practical applications, in particular in audio signal processing.…
Generative models have demonstrated strong performance in conditional settings and can be viewed as a form of data compression, where the condition serves as a compact representation. However, their limited controllability and…
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.…
Sparse representations have emerged as a powerful tool in signal and information processing, culminated by the success of new acquisition and processing techniques such as Compressed Sensing (CS). Fusion frames are very rich new signal…
We develop sub-Nyquist sampling systems for analog signals comprised of several, possibly overlapping, finite duration pulses with unknown shapes and time positions. Efficient sampling schemes when either the pulse shape or the locations of…
In this paper we address the problem of constructing a feature extractor which combines Mallat's scattering transform framework with time-frequency (Gabor) representations. To do this, we introduce a class of frames, called uniform covering…
In this paper we propose a method for automatic local time adap- tation of the spectrogram of an audio signal, based on its decomposition within a Gabor multi-frame. The sparsity of the analyses within each individual frame is evaluated…
Fusion frames are collection of subspaces which provide a redundant representation of signal spaces. They generalize classical frames by replacing frame vectors with frame subspaces. This paper considers the sparse recovery of a signal from…
Although frames, which are a generalization of bases, are important tools used in signal processing, their potential in other fields of engineering and applied mathematics (e.g. acoustics) has not been fully explored yet. Gabor frames, that…
Gabor frames have interested many mathematicians and physicists due to their potential applications in time-frequency analysis, in particular, signal processing. A Gabor system is a collection of vectors which is obtained by applying…
This paper studies the problem of clustering in the two-component Gaussian mixture model where the centers are separated by $2\Delta$ for some $\Delta>0$. We characterize the exact phase transition threshold, given by $$ \bar{\Delta}_n^{2}…
We present a time-frequency framework adapted to dispersive phase functions via a subdyadic geometry in phase space. On top of this geometry we construct stable Gabor frames with quantitative control of overlap, almost orthogonality, and…
Sparse representation leads to an efficient way to approximately recover a signal by the linear composition of a few bases from a learnt dictionary, based on which various successful applications have been achieved. However, in the scenario…
We construct frames adapted to a given cover of the time-frequency or time-scale plane. The main feature is that we allow for quite general and possibly irregular covers. The frame members are obtained by maximizing their concentration in…
The quantum mechanical harmonic oscillator Hamiltonian generates a one-parameter unitary group W(\theta) in L^2(R) which rotates the time-frequency plane. In particular, W(\pi/2) is the Fourier transform. When W(\theta) is applied to any…