Convex Optimization Based Bit Allocation for Light Field Compression under Weighting and Consistency Constraints

Compared with conventional image and video, light field images introduce the weight channel, as well as the visual consistency of rendered view, information that has to be taken into account when compressing the pseudo-temporal-sequence (PTS) created from light field images. In this paper, we propose a novel frame level bit allocation framework for PTS coding. A joint model that measures weighted distortion and visual consistency, combined with an iterative encoding system, yields the optimal bit allocation for each frame by solving a convex optimization problem. Experimental results show that the proposed framework is effective in producing desired distortion distribution based on weights, and achieves up to 24.7% BD-rate reduction comparing to the default rate control algorithm.Comment: published in IEEE Data Compression Conference, 201

Hankel determinants, Pad\'e approximations, and irrationality exponents

The irrationality exponent of an irrational number $\xi$, which measures the approximation rate of $\xi$ by rationals, is in general extremely difficult to compute explicitly, unless we know the continued fraction expansion of $\xi$. Results obtained so far are rather fragmentary, and often treated case by case. In this work, we shall unify all the known results on the subject by showing that the irrationality exponents of large classes of automatic numbers and Mahler numbers (which are transcendental) are exactly equal to $2$. Our classes contain the Thue--Morse--Mahler numbers, the sum of the reciprocals of the Fermat numbers, the regular paperfolding numbers, which have been previously considered respectively by Bugeaud, Coons, and Guo, Wu and Wen, but also new classes such as the Stern numbers and so on. Among other ingredients, our proofs use results on Hankel determinants obtained recently by Han.Comment: International Mathematics Research Notices 201