Adrian S. Lewis

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The 2-D orthogonal wavelet transform decomposes images into both spatial and spectrally local coefficients. The transformed coefficients were coded hierarchically and individually quantized in accordance with the local estimated noise sensitivity of the human visual system (HVS). The algorithm can be mapped easily onto VLSI. For the Miss America and Lena(More)
Let f be a continuous function on Rn, and suppose f is continuously differentiable on an open dense subset. Such functions arise in many applications, and very often minimizers are points at which f is not differentiable. Of particular interest is the case where f is not convex, and perhaps not even locally Lipschitz, but is a function whose gradient is(More)
We study randomized variants of two classical algorithms: coordinate descent for systems of linear equations and iterated projections for systems of linear inequalities. Expanding on a recent randomized iterated projection algorithm of Strohmer and Vershynin for systems of linear equations, we show that, under appropriate probability distributions, the(More)
We prove that if two smooth manifolds intersect transversally, then the method of alternating projections converges locally at a linear rate. We bound the speed of convergence in terms of the angle between the manifolds, which in turn we relate to the modulus of metric regularity for the intersection problem, a natural measure of conditioning. We discuss a(More)
Using convex analysis, this paper gives a systematic and uniied treatment for the existence of a global error bound for a convex inequality system. We establish a necessary and suucient condition for a closed convex set deened by a closed proper convex function to possess a global error bound in terms of a natural residual. We derive many special cases of(More)
We study convex programs that involve the minimization of a convex function over a convex subset of a topological vector space, subject to a finite number of linear inequalities. We develop the notion of the quasi relative interior of a convex set, an extension of the relative interior in finite dimensions. We use this idea in a constraint qualification for(More)
In Part I of this work we derived a duality theorem for partially finite convex programs, problems for which the standard Slater condition fails almost invariably. Our result depended on a constraint qualification involving the notion of quasi relative interior. The derivation of the primal solution from a dual solution depended on the differentiability of(More)
Given a real-analytic function f : Rn → R and a critical point a ∈ Rn, the Lojasiewicz inequality asserts that there exists θ ∈ [ 1 2 , 1) such that the function |f − f(a)|θ ‖∇f‖−1 remains bounded around a. In this paper, we extend the above result to a wide class of nonsmooth functions (that possibly admit the value +∞), by establishing an analogous(More)
The luminal and basal epithelial cells in the human mammary gland can be distinguished in tissue sections on the basis of the pattern of keratins they express. Moreover, the invasive cells in primary carcinomas show a keratin profile that corresponds to that of the dominant luminal cell (7, 8, 18, 19). When homogeneous populations of luminal epithelial(More)