抗雜訊壓縮感知還原演算法及硬體架構設計

Robust Reconstruction Algorithm and Hardware Design for Compressive Sensing Systems

黃乃珊(Nai-Shan Huang)

指導教授 ： 吳安宇

國立臺灣大學/電機資訊學院/電子工程學研究所/碩士(2014年)

https://doi.org/10.6342/NTU.2014.10005

摘要

壓縮感知是近年來熱門的研究方向，它希望可以減少訊號的取樣率，使其低於傳統奈奎斯理論的取樣量，然後將訊號由這些較少的取樣率中還原。壓縮感知的想法建立在兩個基礎上：訊號的稀疏性和取樣的非相關性。首先，大部分自然界中的訊號皆具有稀疏性，或是說他們在適當的基底中都是可以被壓縮的。另外，取樣的方法必須讓基底中每一個元素都有同樣的機率被取樣到。壓縮感知的研究主要可以分為取樣及還原，本篇論文將會著重在訊號還原的部分。
壓縮感知的訊號還原主要在解一個未定訊號的問題。基本上，我們希望可以找到一個具有最稀疏性的還原訊號。大部分壓縮感知的演算法都具有很高的運算複雜度，且他們忽略在實際應用會遇到的雜訊問題，並且也很難被實現在硬體上。因此，我們希望可以提出一個適合實現在硬體的壓縮感知還原演算法，並且演算法具有抗雜訊、低運算複雜度的特性。
我們將可適性濾波器的演算法引進到壓縮感知的還原問題中，提出一個以可適性濾波器為基礎的還原演算法。利用可適性濾波器的特性，我們提出的演算法具有較好的抗雜訊特性，且在高維度的應用中可以有比現在演算法更低的運算複雜度。並且，我們將提出的還原演算法實現在硬體中，我們提出的還原引擎可以在低成本的情況下達到高吞吐量的特性，且其可以應用在具有不同稀疏性的輸入訊號中。本篇論文提出的還原演算法及還原引擎可以幫助壓縮感知應用在更多不同的實際問題中。

關鍵字

壓縮感知 ； 訊號還原 ； 可適性濾波器

並列摘要

Compressive sensing is a novel research and attracts growing attention recently. Compressive sensing aims to measures signals with fewer samples than Nyquist theorem, and recover signals from these few samples. The idea of compressive sensing is based on two features. One is that natural signals are usually sparse, which means signals are compressible on proper basis. The other is that the sample scheme should sample at every component of the basis with equal probability. Compressive sensing is composed two parts: incoherent sampling and sparse reconstruction. We will focus on reconstruction in this work.
The reconstruction of compressive sensing deals with an underdetermined problem. Generally, the reconstruction attempts to find an approximate solution with least L1 value. Most all reconstruction algorithms have high computational complexity, ignore noise issue in real application, and are hard to implement in hardware. Thus, we propose a hardware friendly reconstruction algorithm with noise resilience and low complexity.
We introduce adaptive filters to reconstruction problem in compressive sensing. A robust reconstruction algorithm based on adaptive filter is proposed. With the characteristic of adaptive filters, proposed algorithm has better noise resilience. Moreover, the complexity of proposed algorithms is low and has advantages in high dimension cases. Also, we implement the proposed reconstruction algorithm with chip implementation. Proposed reconstruction engine can achieve high throughput rate under low cost. Furthermore, proposed hardware architecture is reconfigurable for different sparsity. In conclusion, proposed reconstruction algorithm and proposed reconstruction engines can help compressive sensing suit for more applications.

並列關鍵字

compressive sensing ； signal reconstruction ； adaptive filter

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