Near-Optimal Encoding for Sigma-Delta Quantization of Finite Frame Expansions
Near-Optimal Encoding for Sigma-Delta Quantization of Finite Frame Expansions
复制标题
有限帧展开的 Sigma-Delta 量化的近乎最优编码
DOI：
--
复制
发表时间：
2013
影响因子：
1.2
通讯作者：
Rayan Saab
中科院分区：
文献类型：
--
作者：
M. Iwen;Rayan Saab
在本文中，我们研究了对有限帧扩展的粗Σ-Δ量化产生的比特流进行编码（即，超定表示）的向量。我们表明，对于广泛的有限帧，包括随机帧和分段平滑帧，存在一个简单的编码算法，只作用于Σ-Δ位流和相关的解码算法，一起产生一个近似误差，指数衰减的位数使用。编码策略包括将离散随机运算符应用于Σ-Δ比特流并将二进制码字分配给结果。重建过程基本上是线性的，等价于求解最小二乘最小化问题。
In this paper we investigate encoding the bit-stream resulting from coarse Sigma-Delta quantization of finite frame expansions (i.e., overdetermined representations) of vectors. We show that for a wide range of finite-frames, including random frames and piecewise smooth frames, there exists a simple encoding algorithm—acting only on the Sigma-Delta bit stream—and an associated decoding algorithm that together yield an approximation error which decays exponentially in the number of bits used. The encoding strategy consists of applying a discrete random operator to the Sigma-Delta bit stream and assigning a binary codeword to the result. The reconstruction procedure is essentially linear and equivalent to solving a least squares minimization problem.