Related papers: Procrustes problems and Parseval quasi-dual frames

This work aims to give non-asymptotic results for estimating the first principal component of a multivariate random process. We first define the covariance function and the covariance operator in the multivariate case. We then define a…

We consider finite frames with high redundancy so that if half the terms transmitted from the sender are randomly deleted during transmission, then on average, the receiver can still recover the signal to within a high level of accuracy.…

Signal models formed as linear combinations of few atoms from an over-complete dictionary or few frame vectors from a redundant frame have become central to many applications in high dimensional signal processing and data analysis. A core…

This paper investigates two parameters that measure the coherence of a frame: worst-case and average coherence. We first use worst-case and average coherence to derive near-optimal probabilistic guarantees on both sparse signal detection…

We present a way to construct Parseval frames of piecewise constant functions for $L^2[0,1]$. The construction is similar to the generalized Walsh bases. It is based on iteration of operators that satisfy a Cuntz-type relation, but without…

This paper deals with the possibility of transforming a weakly measurable function in a Hilbert space into a continuous frame by a metric operator, i.e., a strictly positive self-adjoint operator. A necessary condition is that the domain of…

In recent work, redressed warped frames have been introduced for the analysis and synthesis of audio signals with non-uniform frequency and time resolutions. In these frames, the allocation of frequency bands or time intervals of the…

We propose an extended primal-dual algorithm framework for solving a general nonconvex optimization model. This work is motivated by image reconstruction problems in a class of nonlinear imaging, where the forward operator can be formulated…

The prime focus of this paper is the study of optimal duals of a given finite frame as well as optimal dual pairs, in the context of probability modelled erasures of frame coefficients. We characterize optimal dual frames (and dual pairs)…

It is known that the frame error rate of turbo codes on quasi-static fading channels can be accurately approximated using the convergence threshold of the corresponding iterative decoder. This paper considers quasi-static fading channels…

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…

This paper addresses the task of learning convex regularizers to guide the reconstruction of images from limited data. By imposing that the reconstruction be amplitude-equivariant, we narrow down the class of admissible functionals to those…

We first establish a kernel theorem that characterizes all linear shift-invariant (LSI) operators acting on discrete multicomponent signals. This result naturally leads to the identification of the Parseval convolution operators as the…

This investigation seeks to establish the practicality of numerical frame approximations. Specifically, it develops a new method to approximate the inverse frame operator and analyzes its convergence properties. It is established that…

We consider frames F in a given Hilbert space, and we show that every F may be obtained in a constructive way from a reproducing kernel and an orthonormal basis in an ambient Hilbert space. The construction is operator-theoretic, building…

Sparse channel estimation for massive multiple-input multiple-output systems has drawn much attention in recent years. The required pilots are substantially reduced when the sparse channel state vectors can be reconstructed from a few…

Our work considers the optimization of the sum of a non-smooth convex function and a finite family of composite convex functions, each one of which is composed of a convex function and a bounded linear operator. This type of problem is…

Finding the optimal dual frame and optimal dual pair for signal reconstruction, which can minimize the reconstruction error when erasure occurs during data transmission, is a deep rooted problem from the perspective of frame theory. In this…

Parseval and equal-norm frames play a fundamental role in frame theory and signal processing. In this work, we prove non-asymptotic concentration bounds showing that random equal-norm frames are nearly Parseval with high probability, and…

We study the feasibility of short finite impulse response (FIR) synthesis for perfect reconstruction (PR) in generic FIR filter banks. Among all PR synthesis banks, we focus on the one with the minimum filter length. For filter banks with…