Discrimination of form in images corrupted by speckle

The problem investigated is that of a human observer having to distinguish between certain specified geometrical forms corrupted by speckle-an idealization of the problem of a scientist studying a synthetic aperture radar map. Specifically, the cases of two simple alternative forms and of two and four orientations of a simple form have been considered. A theoretical model is developed for the observer's decision process by analogy with optimal receiver theory, and the probability of a correct decision is related to form parameters like size, contrast, and looks. These calculations are verified by psychophysical experiments using computer-simulated pictures

Effect of ambiguities on SAR picture quality

The degradation of picture quality is studied for a high-resolution, large-swath SAR mapping system subjected to speckle, additive white Gaussian noise, and range and azimuthal ambiguities occurring because of the non-finite antenna pattern produced by a square aperture antenna. The effect of the azimuth antenna pattern was accounted for by calculating the aximuth ambiguity function. Range ambiguities were accounted for by adding appropriate pixels at a range separation corresponding to one pulse repetition period, but attenuated by the antenna pattern. A method of estimating the range defocussing effect which arises from the azimuth matched filter being a function of range is shown. The resulting simulated picture was compared with one degraded by speckle and noise but no ambiguities. It is concluded that azimuth ambiguities don't cause any noticeable degradation but range ambiguities might

Deterministic Identity Testing for Sum of Read-Once Oblivious Arithmetic Branching Programs

A read-once oblivious arithmetic branching program (ROABP) is an arithmetic branching program (ABP) where each variable occurs in at most one layer. We give the first polynomial time whitebox identity test for a polynomial computed by a sum of constantly many ROABPs. We also give a corresponding blackbox algorithm with quasi-polynomial time complexity $n^{O(\log n)}$. In both the cases, our time complexity is double exponential in the number of ROABPs. ROABPs are a generalization of set-multilinear depth-$3$ circuits. The prior results for the sum of constantly many set-multilinear depth-$3$ circuits were only slightly better than brute-force, i.e. exponential-time. Our techniques are a new interplay of three concepts for ROABP: low evaluation dimension, basis isolating weight assignment and low-support rank concentration. We relate basis isolation to rank concentration and extend it to a sum of two ROABPs using evaluation dimension (or partial derivatives).Comment: 22 pages, Computational Complexity Conference, 201

Effect of pixel dimensions on SAR picture quality

In an SAR mapping system, the product of looks per pixel and number of pixels in the scene is kept constant. Assuming that the returns from all resolution cells obey Rayleigh statistics, the expression for pixel SNR incorporating both speckle and additive white Gaussian noise was derived. It is shown that it is possible to use fine resolution and leave the large-area estimate slightly but not much worse than if a larger pixel size had been initially decided upon

Vibrational transition probabilities of the bands of the barium oxide (A 1SIGMA-​X 1SIGMA) system

The band spectrum of BaO has been obtained by spraying BaCl2 soln. into a flame. The integrated intensities of the bands have been detd. by photographic photometry. The exptl. results along with the theoretically computed Franck-​Condon factors have been used to evaluate a relation between Re, the electronic transition moment, and r, the internuclear sepn., in the form, Re(r v'v'') = const.(1 - 0.536r)​. This relation has been used to obtain improved Franck-​Condon factors. The theoretically computed Franck-​Condon factors, with and without the inclusion of Re variation, have been compared with the exptl. band strengths

Identity Testing for Constant-Width, and Commutative, Read-Once Oblivious ABPs

We give improved hitting-sets for two special cases of Read-once Oblivious Arithmetic Branching Programs (ROABP). First is the case of an ROABP with known variable order. The best hitting-set known for this case had cost (nw)^{O(log(n))}, where n is the number of variables and w is the width of the ROABP. Even for a constant-width ROABP, nothing better than a quasi-polynomial bound was known. We improve the hitting-set complexity for the known-order case to n^{O(log(w))}. In particular, this gives the first polynomial time hitting-set for constant-width ROABP (known-order). However, our hitting-set works only over those fields whose characteristic is zero or large enough. To construct the hitting-set, we use the concept of the rank of partial derivative matrix. Unlike previous approaches whose starting point is a monomial map, we use a polynomial map directly. The second case we consider is that of commutative ROABP. The best known hitting-set for this case had cost d^{O(log(w))}(nw)^{O(log(log(w)))}, where d is the individual degree. We improve this hitting-set complexity to (ndw)^{O(log(log(w)))}. We get this by achieving rank concentration more efficiently