ﮐﺎرﺑﺮد روش ﺗﮑﻤﯿﻞ ﺗﻨﺴﻮري ﺑﻬﯿﻨﻪ ﺳﺎزي ﺷﺪه ﺗﮏ ﺑﯿﺘﯽ در ﺑﺎزﯾﺎﻓﺖ ﺗﺼﺎوﯾﺮ دﯾﺠﯿﺘﺎﻟﯽ ﻣﺨﺪوش

{Application of the optimized 1-bit tensor completion method in the recovery of noisy digital images

ﭼﮑﯿﺪه: داده ﻫﺎي ﺳﺎﺧﺘﺎري ﺗﻨﺴﻮري ﻣﺮﺗﺒﻪ ﺑﺎﻻ در ﺑﺴﯿﺎري از ﺳﻨﺎرﯾﻮﻫﺎي ﺗﺼﻮﯾﺮﺑﺮداري ﻧﻈﯿﺮ ﺗﺼﻮﯾﺮﺑﺮداري ﻓﺮاﻃﯿﻔﯽ و وﯾﺪﯾﻮﻫﺎي رﻧﮕﯽ، ﺑﻪ ﮐﺎر ﻣﯽ روﻧﺪ. ﺑﺎزﯾﺎﺑﯽ ﯾﮏ ﺗﻨﺴﻮر از ﯾﮏ ﻣﺠﻤﻮﻋﻪ ﻧﺎﻗﺺ از درآﯾﻪ ﻫﺎ، ﮐﻪ ﺗﮑﻤﯿﻞ ﺗﻨﺴﻮري ﻧﺎﻣﯿﺪه ﻣﯽ ﺷﻮد، درزﻣﯿﻨﻪ ﻫﺎﯾﯽ ﻧﻈﯿﺮ ﭘﺮدازش ﺗﺼﺎوﯾﺮ دﯾﺠﯿﺘﺎل و ﻓﺸﺮده ﺳﺎزي ﮐﺎرﺑﺮدﻫﺎي ﻓﺮاواﻧﯽ دارد. در ﺗﮑﻤﯿﻞ ﺗﻨﺴﻮري، ﻋﻼوه ﺑﺮ ﻧﺎﻗﺺ ﺑﻮدن داده ﻫﺎي ﻣﺸﺎﻫﺪه ﺷﺪه، ﻣﺴﺎﻟﻪ دﯾﮕﺮ ﮐﻤﯽ ﺳﺎزي درآﯾﻪ ﻫﺎ اﺳﺖ. ﮐﻤﯽ ﺳﺎزي ﻣﺮﺣﻠﻪ اي ﻣﻬﻢ ﺑﺮاي اﻧﺘﻘﺎل و ذﺧﯿﺮه ﺳﺎزي داده ﻫﺎي ﺑﻌﺪ ﺑﺎﻻ ﺑﻪ ﻣﻨﻈﻮر ﮐﺎﻫﺶ ﻧﯿﺎز ﺑﻪ ذﺧﯿﺮه ﺳﺎزي و ﺻﺮﻓﻪ ﺟﻮﯾﯽ در ﻣﺼﺮف اﻧﺮژي اﺳﺖ. در اﯾﻦ ﺟﺎ، روﺷﯽ ﺟﺪﯾﺪ ﺑﺮاي ﺑﺎزﯾﺎﻓﺖ ﺗﻨﺴﻮرﻫﺎي رﺗﺒﻪ ﭘﺎﯾﯿﻦ از ﺗﻌﺪاد اﻧﺪﮐﯽ اﻧﺪازه ﮔﯿﺮي ﻫﺎي دودوﯾﯽ )ﺗﮏ ﺑﯿﺘﯽ( اراﺋﻪ ﻣﯽ ﺷﻮد. روش ﺗﮑﻤﯿﻞ ﺗﻨﺴﻮري ﺗﮏ ﺑﯿﺘﯽ، ﻣﺘﮑﯽ ﺑﺮ ﮐﺎرﺑﺮد ﺗﮑﻤﯿﻞ ﺗﻨﺴﻮري در ﻧﺴﺨﻪ ﻫﺎي ﻣﺎﺗﺮﯾﺴﯽ ﺷﺪه ﺑﺎ داده ﻫﺎي دودوﯾﯽ در ﺗﻨﺴﻮر زﻣﯿﻨﻪ اي داده ﻫﺎ اﺳﺖ. ﻧﺘﺎﯾﺞ آزﻣﺎﯾﺸﯽ در ﺗﺼﺎوﯾﺮ ﻓﺮاﻃﯿﻔﯽ ﻧﺸﺎن دﻫﻨﺪه آن اﺳﺖ ﮐﻪ ﻋﻤﻠﯿﺎت ﻣﺴﺘﻘﯿﻢ ﺑﺎ اﻧﺪازه ﮔﯿﺮي دودوﯾﯽ، ﺑﻪ ﺟﺎي ﻣﻘﺎدﯾﺮ ﺣﻘﯿﻘﯽ آن ﻫﺎ ﻣﻨﺠﺮ ﺑﻪ ﺧﻄﺎي ﺑﺎزﯾﺎﻓﺖ ﮐﻢ ﺗﺮي ﻣﯽ ﺷﻮد. در اﯾﻦ ﺟﺎ ﯾﮏ ﺗﻨﺴﻮر ﻣﺮﺗﺒﻪ ﺳﻮم داده ﺷﺪه ﺑﺎ درآﯾﻪ ﻫﺎي دودوﯾﯽ ﺑﺎزﯾﺎﻓﺖ ﻣﯽ ﺷﻮد. در ﻋﻤﻞ ﺗﻨﺴﻮر را ﺑﻪ ﺻﻮرت ﯾﮏ ﻓﺮاﻣﺎﺗﺮﯾﺲ ﺳﻪ ﺗﺎﯾﯽ ﺑﺎز ﻧﻤﻮده و اﻟﮕﻮرﯾﺘﻢ ﺗﮑﻤﯿﻞ ﺗﻨﺴﻮري ﮐﻤﯽ ﺳﺎزي ﺷﺪه را ﺑﺮ ﻫﻤﻪ ﻣﺪل ﻫﺎي ﻣﺎﺗﺮﯾﺴﯽ ﺗﻨﺴﻮر ﻣﺰﺑﻮر ﺑﻪ ﮐﺎر ﻣﯽ ﺑﺮﯾﻢ. ﻓﻀﺎي داده اي در اﯾﻦ ﺟﺎ ﺗﺼﺎوﯾﺮ ﻓﺮاﻃﯿﻔﯽ ﻣﺎﻫﻮاره اي ﺑﺎ ﻫﺪف ﺑﺎزﯾﺎﻓﺖ ﺗﺼﺎوﯾﺮ ﻣﺨﺪوش ﺷﺪه اﺳﺖ.

Higher-order tensor structured data appear in many imaging scenarios, including hyperspectral imaging and colorful video. The recovery of a tensor from an incomplete set of its entries, known as tensor completion (TC), is significant in applications like compression. Moreover, in many illustrations, observations are not only incomplete but also highly quantized. Quantization is a critical step for high dimensional data transmission and storage in order to reduce storage requirements and power consumption, especially for energy-limited systems. In this paper, we propose a novel approach for the recovery of low-rank tensors from a small number of binary (1-bit) measurements. The proposed method called $1- bit$ Tensor Completion relies on the application of 1-bit matrix completion over different matricizations of the underlying tensor. Experimental results on hyperspectral images confirm that directly operating with the binary measurements, rather than treating them as real values, results in lower recovery error. Here a given third-order tensor with binary arrays is recovered. In practice, we open the tensor as a 3-matrix and apply the quantified tensor completion algorithm to all models of the matrix tensor. The data space here is distorted satellite spectral images for the purpose of image recovery.