ISTA-Net: Interpretable Optimization-Inspired Deep Network for Image Compressive Sensing

With the aim of developing a fast yet accurate algorithm for compressive sensing (CS) reconstruction of natural images, we combine in this paper the merits of two existing categories of CS methods: the structure insights of traditional optimization-based methods and the speed of recent network-based ones. Specifically, we propose a novel structured deep network, dubbed ISTA-Net, which is inspired by the Iterative Shrinkage-Thresholding Algorithm (ISTA) for optimizing a general $\ell_1$ norm CS reconstruction model. To cast ISTA into deep network form, we develop an effective strategy to solve the proximal mapping associated with the sparsity-inducing regularizer using nonlinear transforms. All the parameters in ISTA-Net (\eg nonlinear transforms, shrinkage thresholds, step sizes, etc.) are learned end-to-end, rather than being hand-crafted. Moreover, considering that the residuals of natural images are more compressible, an enhanced version of ISTA-Net in the residual domain, dubbed {ISTA-Net}$^+$, is derived to further improve CS reconstruction. Extensive CS experiments demonstrate that the proposed ISTA-Nets outperform existing state-of-the-art optimization-based and network-based CS methods by large margins, while maintaining fast computational speed. Our source codes are available: \textsl{http://jianzhang.tech/projects/ISTA-Net}.Comment: 10 pages, 6 figures, 4 Tables. To appear in CVPR 201

English Conversational Telephone Speech Recognition by Humans and Machines

One of the most difficult speech recognition tasks is accurate recognition of human to human communication. Advances in deep learning over the last few years have produced major speech recognition improvements on the representative Switchboard conversational corpus. Word error rates that just a few years ago were 14% have dropped to 8.0%, then 6.6% and most recently 5.8%, and are now believed to be within striking range of human performance. This then raises two issues - what IS human performance, and how far down can we still drive speech recognition error rates? A recent paper by Microsoft suggests that we have already achieved human performance. In trying to verify this statement, we performed an independent set of human performance measurements on two conversational tasks and found that human performance may be considerably better than what was earlier reported, giving the community a significantly harder goal to achieve. We also report on our own efforts in this area, presenting a set of acoustic and language modeling techniques that lowered the word error rate of our own English conversational telephone LVCSR system to the level of 5.5%/10.3% on the Switchboard/CallHome subsets of the Hub5 2000 evaluation, which - at least at the writing of this paper - is a new performance milestone (albeit not at what we measure to be human performance!). On the acoustic side, we use a score fusion of three models: one LSTM with multiple feature inputs, a second LSTM trained with speaker-adversarial multi-task learning and a third residual net (ResNet) with 25 convolutional layers and time-dilated convolutions. On the language modeling side, we use word and character LSTMs and convolutional WaveNet-style language models