We develop a framework for post model selection inference, via marginal screening, in linear regression. At the core of this framework is a result that characterizes the exact distribution of linear functions of the response y, conditional on the model being selected (“condition on selection" framework). This allows us to construct valid confidence intervals and hypothesis tests for regression ...

As an extension of orthogonal matching pursuit (OMP) improving the recovery performance of sparse signals, generalized OMP (gOMP) has recently been studied in the literature. In this paper, we present a new analysis of the gOMP algorithm using restricted isometry property (RIP). We show that if the measurement matrix Φ ∈ R satisfies the RIP with δmax{9,S+1}K ≤ 1 8 , then gOMP performs stable re...

Generalized Orthogonal Matching Pursuit (gOMP) is a natural extension of OMP algorithm where unlike OMP, it may select N(≥ 1) atoms in each iteration. In this paper, we demonstrate that gOMP can successfully reconstruct a K-sparse signal from a compressed measurement y = Φx by K iteration if the sensing matrix Φ satisfies restricted isometry property (RIP) of order NK where δNK < √ N √ K+2 √ N ...

In this letter, we first construct a counter example to show that for any given positive integer K ≥ 2 and for any 1 √ K+1 ≤ t < 1, there always exist a K−sparse x and a matrix A with the restricted isometry constant δK+1 = t such that the OMP algorithm fails in K iterations. Secondly, we show that even when δK+1 = 1 √ K+1 , the OMP algorithm can also perfectly recover every K−sparse vector x f...

Over-complete signal decomposition has been shown to be an efficient technique for coding disparity compensated residual images in stereo image pairs. This paper presents a residual image coding scheme based on a recently proposed MP-based coding scheme called SOW. The proposed scheme decomposes an orthogonal matching pursuit process into two stages. In different stages, dictionaries of differe...

In this paper, we present an algorithm for seismic source wavelet estimation that is based on seismic time frequency spectral decomposition with matching pursuit technique. The main assumption of this algorithm is that the source wavelet is stationary for single wavelet estimation in a selected time window and that the source wavelet has normalized energy to avoid scale ambiguity between reflec...

In this paper, we present a method to decompose visual motion represented by computed optical flow using an overcomplete dictionary of space frequency atoms. This is accomplished by a modified matching pursuit procedure which successively selects space and frequency localized atoms from this dictionary. In effect, this decomposition reveals the structure of optical flow field such that areas wi...

When small objects move in a scene, we keep them foveated with smooth pursuit eye movements. Although large objects such as people and animals are common, it is nonetheless unknown how we pursue them since they cannot be foveated. It might be that the brain calculates an object's centroid, and then centers the eyes on it during pursuit as a foveation mechanism might. Alternatively, the brain me...

The problem of optimal approximation of function with a linear expansion using overcomplete dictionary of non-orthogonal waveforms is NP-hard. Matching pursuit, introduced by Mallat and Zhang, is a greedy sub-optimal algorithm for finding an approximate solution to the above problem. This technique has been adopted by Neff and Zakhor as an alternative to the conventional DCT-based method for co...

The objective of image coding is to reduce the number of bits needed to represent an image, while making as few as possible perceptual distortion to the image. Images coded at low bit-rates, say below 0.5bpp, bear the loss of details and sharpness, as well as various artifacts which are perceptually objectionable. On the other hand, with the need for transmission and storage of more and larger ...