SC-CSNet-TP: A Smoothed Convolutional Compressed Sensing Network With Ternary Projection

An end-to-end compressed sensing (CS) framework, smoothed convolutional CS network with ternary projection (SC-CSNet-TP), has been proposed in this article to deal with problems, including unacceptable cost (i.e., high computational complexity and vast storage requirement), blocking artifact incurred by block CS (BCS), checkerboard artifacts, etc., in order to realize higher reconstruction quality at lower cost. SC-CSNet-TP adopts the framework of CSNet, which consists of a sampling network, an initial reconstruction network, and a deep reconstruction network, and introduces more improvements: 1) sampling is actually a procedure of BCS and can be implemented by convolutions, whose filters form the measurement matrix. In order to balance the precision and hardware pressure, we take ternary measurement matrices into account, which are obtained by pruning binarization process through the self-attention mechanism; 2) the initial reconstruction network focuses on mitigating the blocking artifacts. Blocks restored by inverse convolutions from compressed measurements are smoothed by smoothed projected Landweber (SPL), followed by depth separable convolutions to exploit interblock semantic correlation, with the output upscaled by pixel shuffle to form an initially reconstructed image; and 3) the deep reconstruction network is made of two base blocks interpolated by a dilated convolution, which captures multiscale contextual information to avoid checkerboard artifacts possibly incurred by dilated convolution, and further refines the initial reconstructed image. Experimental results show that the quality of reconstruction by means of SC-CSNet-TP reaches a satisfactory level, e.g., the average peak signal-to-noise ratio on Set11 has approximate 6% improvement compared with that of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\text {DR}^{2}\text {-Net}$ </tex-math></inline-formula> when the sampling rate is 0.25.