Related papers: Tight frames, partial isometries, and signal recon…
The characterization of a binary function by partial frequency information is considered. We show that it is possible to reconstruct binary signals from incomplete frequency measurements via the solution of a simple linear optimization…
In this paper we ask when it is possible to transform a given sequence into a frame or a lower semi frame by multiplying the elements by numbers. In other words, we ask when a given sequence is a weighted frame or a weighted lower semi…
Continuing the ideas from our previous paper, we construct Parseval frames of weighted exponential functions for self-affine measures.
In this note we study frame-related properties of a sequence of functions multiplied by another function. In particular we study frame and Riesz basis properties. We apply these results to sets of irregular translates of a bandlimited…
An architecture for hardware realization of a system for sparse signal reconstruction is presented. The threshold based reconstruction method is considered, which is further modified in this paper to reduce the system complexity in order to…
An important yet challenging problem in understanding indoor scene is recovering indoor frame structure from a monocular image. It is more difficult when occlusions and illumination vary, and object boundaries are weak. To overcome these…
We develop the theory of frames and Parseval frames for finite-dimensional vector spaces over the binary numbers. This includes characterizations which are similar to frames and Parseval frames for real or complex Hilbert spaces, and the…
In this paper, an algorithm based on polyphase matrix for constructing a pair of orthogonal wavelet frames is suggested, and a general form for all orthogonal tight wavelet frames on local fields of positive characteristic is described.…
We present an improved Bayesian framework for performing inference of affine transformations of constrained functions. We focus on quadrature with nonnegative functions, a common task in Bayesian inference. We consider constraints on the…
This paper deals with structural issues concerning wavelet frames and their dual frames. It is known that there exist wavelet frames $\{a^{j/2}\psi( a^j\cdot -kb)\}_{j,k\in \mathbb Z}$ in $L^2(\mathbb R)$ for which no dual frame has wavelet…
We study the properties of a set of vectors called tight frames that obtained as the orthogonal projection of some orthonormal basis of $\R^n$ onto $\R^k.$ We show that a set of vectors is a tight frame if and only if the set of all cross…
The task of reconstructing a low rank matrix from incomplete linear measurements arises in areas such as machine learning, quantum state tomography and in the phase retrieval problem. In this note, we study the particular setup that the…
In information fusion, one is often confronted with the following problem: given a preexisting set of measurements about an unknown quantity, what new measurements should one collect in order to accomplish a given fusion task with optimal…
Recently, sparsity-based algorithms are proposed for super-resolution spectrum estimation. However, to achieve adequately high resolution in real-world signal analysis, the dictionary atoms have to be close to each other in frequency,…
A signal is sparse in one of its representation domain if the number of nonzero coefficients in that domain is much smaller than the total number of coefficients. Sparse signals can be reconstructed from a very reduced set of…
This article is written to serve as an introduction and survey of imaging with synthetic aperture radar (SAR). The reader will benefit from having some familiarity with harmonic analysis, electromagnetic radiation, and inverse problems.…
In many signal processing problems arising in practical applications, we wish to reconstruct an unknown signal from its phaseless measurements with respect to a frame. This inverse problem is known as the phase retrieval problem. For each…
In image morphing, a sequence of plausible frames are synthesized and composited together to form a smooth transformation between given instances. Intermediates must remain faithful to the input, stand on their own as members of the set,…
The paper observes the Hermite and the Fourier Transform domains in terms of Frequency Hopping Spread Spectrum signals sparsification. Sparse signals can be recovered from a reduced set of samples by using the Compressive Sensing approach.…
The ability to efficiently and accurately construct an inverse frame operator is critical for establishing the utility of numerical frame approximations. Recently, the admissible frame method was developed to approximate inverse frame…