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- Kangyu Ni, Somantika Datta, Prasun Mahanti, Svetlana Roudenko, Douglas Cochran
- SIAM J. Imaging Sciences
- 2011

- Somantika Datta, Stephen D. Howard, Douglas Cochran
- ArXiv
- 2009

A geometric perspective is used to derive the entire family of Welch bounds. This perspective unifies a number of observations that have been made regarding tightness of the bounds and their connections to symmetric k-tensors, tight frames, homogeneous polynomials, and tdesigns. Index Terms – Frames, Grammian, Homogeneous polynomials, Symmetric tensors,… (More)

- John J. Benedetto, Somantika Datta
- Adv. Comput. Math.
- 2010

Unimodular waveforms x are constructed on the integers with the property that the autocorrelation of x is one at the origin and zero elsewhere. There are three different constructions: exponentials of the form e2π in θ , sequences taken from roots of unity, and sequences constructed from the elements of real Hadamard matrices. The first is expected and… (More)

We explore the stability of image reconstruction algorithms under deterministic compressed sensing. Recently, we have proposed [1-3] deterministic compressed sensing algorithms for 2D images. These algorithms are suitable when Daubechies wavelets are used as the sparsifying basis. In the initial work, we have shown that the algorithms perform well for… (More)

A recently proposed approach for compressed sensing, or compressive sampling, with deterministic measurement matrices made of chirps is applied to images that possess varying degrees of sparsity in their wavelet representations. The “fast reconstruction” algorithm enabled by this deterministic sampling scheme as developed by Applebaum et al. [1] produces… (More)

- Kangyu Ni, Somantika Datta, Prasun Mahanti, Svetlana Roudenko, Douglas Cochran
- 2010 IEEE International Conference on Acoustics…
- 2010

An image reconstruction algorithm using compressed sensing (CS) with deterministic matrices of second-order Reed-Muller (RM) sequences is introduced. The 1D algorithm of Howard et al. using CS with RM sequences suffers significant loss in speed and accuracy when the degree of sparsity is not high, making it inviable for 2D signals. This paper describes an… (More)

- Somantika Datta, Jesse Oldroyd
- ArXiv
- 2016

Frames have become standard tools in signal processing due to their robustness to transmission errors and their resilience to noise. Equiangular tight frames (ETFs) are particularly useful and have been shown to be optimal for transmission under a certain number of erasures. Unfortunately, ETFs do not exist in many cases and are hard to construct when they… (More)

The method of conventional control of a manipulator, without considering varying effects of robot dynamics, results in degraded response with unnecessary vibrations thus limiting the precision and speed of the end effector. As the column joint is subjected to worst dynamic conditions when all the axes are in motion, simulation of position response of column… (More)

This article gives a procedure to convert a frame which is not a tight frame into a Parseval frame for the same space, with the requirement that each element in the resulting Parseval frame can be explicitly written as a linear combination of the elements in the original frame. Several examples are considered, such as a Fourier frame on a spiral. The… (More)

GivenK > 0 and a positive integerM, the function△K,M (t) = Kmax(1− |t| M , 0) represents an isosceles triangle on the real line R having height K and base 2M. For a given K and M, a constant amplitude sequence is constructed on the integers Z having autocorrelation △K,M restricted to Z. With this setup, a large class of bounded sequences z is shown to… (More)