الگوریتم جدید و مقاوم AMP برای ماتریس‌های غیر iid و گوسی مبتنی بر تئوری بیز در نمونه‌برداری فشرده
محورهای موضوعی : مهندسی برق و کامپیوترفهیمه انصاری رام 1 , مرتضی خادمی 2 , عباس ابراهیمی مقدم 3 , هادی صدوقی یزدی 4
1 - دانشگاه فردوسی مشهد
2 - دانشگاه فردوسی مشهد
3 - دانشگاه فردوسی
4 - دانشگاه فردوسی مشهد
چکیده مقاله :
: الگوریتم تقریب انتقال پیام (AMP) یک الگوریتم تکراری کم‌هزینه برای بازیابی سیگنال در نمونه‌برداری فشرده است. هنگامی که ماتریس نمونه‌بردار دارای مؤلفه‌هایی با توزیع گوسی مستقل و یکسان (iid) باشد، همگرایی AMP با تحلیل ریاضی اثبات می‌شود. اما برای سایر ماتریس‌های نمونه‌بردار به خصوص ماتریس‌های بدحالت، عملکرد این الگوریتم ضعیف شده و حتی ممکن است واگرا شود. این مشکل منجر به محدودیت استفاده از AMP در بعضی کاربردها از جمله تصویربرداری شده است. در این مقاله الگوریتمی جهت اصلاح AMP مبتنی بر تئوری بیز برای ماتریس‌های غیر iid ارائه شده است. نتایج شبیه‌سازی نشان می‌دهد که میزان مقاومت الگوریتم پیشنهادی برای ماتریس‌های غیر iid نسبت به روش‌های پیشین بیشتر می‌باشد. به عبارت دیگر این روش دارای دقت بیشتر در بازیابی است و با تکرار کمتری همگرا خواهد شد.
AMP is a low-cost iterative algorithm for recovering signal in compressed sensing. When the sampling matrix has IID zero-mean Gaussian elements, the convergence of AMP is analytically guaranteed. But for other sampling matrices, especially ill-conditioned matrices, the recovery performance of AMP degrades and even may be diverged. This problem limits the use of AMP in some applications such as imaging. In this paper, a method is proposed for modifying the AMP algorithm based on Bayesian theory for non-IID matrices. Simulation results show better robustness properties of the proposed algorithm for non-IID matrices in comparison with previous works. In other words, the proposed method has more precision in recovery, and converges with less iterations.
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