Nonhomogeneous distributions and optimal quantizers for Sierpiński carpets
نویسنده
چکیده
The purpose of quantization of a probability distribution is to estimate the probability by a discrete probability with finite support. In this paper, a nonhomogeneous probability measure P on R which has support the Sierpiński carpet generated by a set of four contractive similarity mappings with equal similarity ratios has been considered . For this probability measure, the optimal sets of n-means and the nth quantization errors are investigated for all n ≥ 2.
منابع مشابه
Optimal quantizers for probability distributions on nonhomogeneous R-triangles
Quantization of a probability distribution refers to the idea of estimating a given probability by a discrete probability supported by a finite set. In this paper, we have considered a Borel probability measure P on R which has support the R-triangle generated by a set of three contractive similarity mappings on R. For this probability measure, the optimal sets of n-means and the nth quantizati...
متن کاملAsymptotic optimality of scalar Gersho quantizers
In his famous paper [7] Gersho stressed that the codecells of optimal quantizers asymptotically make an equal contribution to the distortion of the quantizer. Motivated by this fact, we investigate in this paper quantizers in the scalar case, where each codecell contributes with exactly the same portion to the quantization error. We show that such quantizers of Gersho type or Gersho quantizers ...
متن کاملQuantizers for the Gamma Distribution and Other Symmetrical Distributions
This paper discusses minimum mean-square error quantization for symmetric distributions. If the distribution satisfies a logconcavity condition, the optimal quantizer is itself symmetric. For the gamma distribution often used to model speech signals, the log-concavity condition is not satisfied. It is shown that for this distribution both the uniformly spaced and the nonuniformly spaced optimal...
متن کاملOptimal quantization for the one-dimensional uniform distribution with Rényi-α-entropy constraints
We establish the optimal quantization problem for probabilities under constrained Rényi-α-entropy of the quantizers. We determine the optimal quantizers and the optimal quan-tization error of one-dimensional uniform distributions including the known special cases α = 0 (restricted codebook size) and α = 1 (restricted Shannon entropy).
متن کاملApproximating vector quantisation by transformation and scalar quantisation
Vector quantization provides better ratedistortion performance over scalar quantization even for a random vector with independent dimensions. However, the design and implementation complexity of vector quantizers is much higher than that of scalar quantizers. To reduce the complexity while achieving performance close to optimal vector quantization and better than scalar quantization, we propose...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- CoRR
دوره abs/1605.02281 شماره
صفحات -
تاریخ انتشار 2016