Encoding-decoding (ED) CNNs have demonstrated state-of-the-art performance for noise reduction over the past years. This has triggered the pursuit of better understanding the inner workings of such architectures, which has led to the theory of deep convolutional framelets (TDCF), revealing important links between signal processing and CNNs. Specifically, the TDCF demonstrates that ReLU CNNs induce low-rankness, since these models often do not satisfy the necessary redundancy to achieve perfect reconstruction (PR). In contrast, this paper explores CNNs that do meet the PR conditions. We demonstrate that in these type of CNNs soft shrinkage and PR can be assumed. Furthermore, based on our explorations we propose the learned wavelet-frame shrinkage network, or LWFSN and its residual counterpart, the rLWFSN. The ED path of the (r)LWFSN complies with the PR conditions, while the shrinkage stage is based on the linear expansion of thresholds proposed Blu and Luisier. In addition, the LWFSN has only a fraction of the training parameters (<1%) of conventional CNNs, very small inference times, low memory footprint, while still achieving performance close to state-of-the-art alternatives, such as the tight frame (TF) U-Net and FBPConvNet, in low-dose CT denoising. 

Noise Reduction in CT Using Learned Wavelet-Frame Shrinkage Networks

The term super-resolution (SR) refers to the applications of enhancing the resolution of an image from low-resolution (LR) to high-resolution (HR). However, for compression purposes, we can intentionally down-sample the image during encoding and then up-sample it with a super-resolution technique at the decoder. Integrating this processing in a compression scheme will allow us to perform improvements through: (1) reducing the loss of information by producing a controlled down-sampling, which preserves the relevant information; (2) increasing the information compensation via a super-resolution technique that enhances the high-frequency components of the reconstructed image. In this paper, we propose a lossy hyperspectral image compression scheme. It combines a 3D wavelet transform with a wavelet learned-based super-resolution technique. The 3D wavelet transform introduces a down-sampling on the hyperspectral image to generate low-resolution (LR) images. This LR sequence is then lossy compressed by the 3D SPIHT encoder at the selected bitrate and produces the bitstream to save or transmit. At the decoder, we do the reconstruction by inverting the 3D SPIHT, which provides us with the approximate coefficients (AC) and corresponding detail coefficients (DC) of the LR image across all sub-bands. Then, we develop a wavelet learning-based SR technique that learns the mapping between the wavelet coefficients using a convolutional neural network (CNN). We use this mapping to invert the down-sampling process and predict the missing detail coefficients. Finally, The LR image and the predicted details coefficients (DC) are used to generate the high-resolution image by applying the inverse 3D wavelet transform. Therefore, we have used the down-sampling and the super-resolution technique as a mechanism to control the compression ratio (CR) and optimize the overall quality of the reconstructed image. The performance of the proposed compression scheme has been evaluated on AVIRIS hyperspectral images and compared with the main existing algorithms. Experimental results show that the proposed algorithm provides a promising performance and can generate high-quality images.

Enhancing hyperspectral image compression using learning-based super-resolution technique

The purpose of this chapter is to describe an alternative approach to the block-transform approach to spatial decorrelation, based on hierarchical subband decompositions. This chapter firstly examines the basic two-channel filter bank structure and then investigates the filter properties that enable perfect reconstruction in the absence of quantization. It then goes on to consider the more general case of multirate filtering, showing how, through the appropriate combination of filters and up- and downsampling operations, critical sampling can be achieved. It next examines specific cases of useful subband and wavelet filters and extends the basic architecture to the case of a multistage (multiscale) decomposition and to two dimensions, as required for image compression applications. Finally, bit allocation strategies and scalability are discussed in the context of the JPEG2000 still image coding standard. Examples are provided throughout.

David R. Bull

Papers

Filter Banks and Wavelet Compression