Memory-Efficient Hierarchical Neural Architecture Search for Image Denoising
Recently, neural architecture search (NAS) methods have attracted much attention and outperformed manually designed architectures on a few high-level vision tasks. In this paper, we propose HiNAS (Hierarchical NAS), an effort towards employing NAS to automatically design effective neural network architectures for image denoising. HiNAS adopts gradient based search strategies and employs operations with adaptive receptive field to build an flexible hierarchical search space. During the search stage, HiNAS shares cells across different feature levels to save memory and employ an early stopping strategy to avoid the collapse issue in NAS, and considerably accelerate the search speed. The proposed HiNAS is both memory and computation efficient, which takes only about 4.5 hours for searching using a single GPU. We evaluate the effectiveness of our proposed HiNAS on two different datasets, namely an additive white Gaussian noise dataset BSD500, and a realistic noise dataset SIM1800. Experimental results show that the architecture found by HiNAS has fewer parameters and enjoys a faster inference speed, while achieving highly competitive performance compared with state-of-the-art methods. We also present analysis on the architectures found by NAS. HiNAS also shows good performance on experiments for image de-raining.
Single image denoising is an important task in low-level computer vision, which restores a clean image from a noisy one. Owing to the fact that noise corruption always occurs in the image sensing process and may degrade the visual quality of collected images, image denoising is needed for various computer vision tasks .
Traditional image denoising methods generally focus on modeling natural image priors and use the priors to restore the clean image, including sparse models [6, 27], Markov random field models , etc. One drawback of these methods is that most of them involve a complex optimization problem and can be time-consuming for inference [5, 10]. Recently, deep learning models have been successfully applied in various computer vision tasks and set new state-of-the-art. Motivated by this, most recent works on image denoising have shifted their approaches to deep learning, which builds a mapping function from noisy images to the desired corresponding clean images with deep learning models and have often outperformed conventional methods significantly [28, 34, 36, 23]. Nonetheless, discovering state-of-the-art neural network architectures requires substantial efforts.
Recently a growing interest is witnessed in developing algorithmic solutions to automate the manual process of architecture design. Architectures automatically found by algorithms have achieved highly competitive performance in high-level vision tasks such as image classification , object detection [9, 37] and semantic segmentation [18, 30]. Inspired by this, here we design algorithms to automatically search for neural architectures efficiently for image denoising tasks. Our main contributions are summarized as follows.
Based on gradient based search algorithms, we propose a memory-efficient hierarchical neural architecture search approach for image denoising, termed HiNAS. To our knowledge, this is the first attempt to apply differentiable architecture search algorithms to low-level vision tasks.
The proposed HiNAS is able to search for both inner cell structures and outer layer widths. It is also memory and computation efficient, taking only about 4.5 hours for searching with a single GPU.
We apply our proposed HiNAS on two denoising datasets of different noise modes for evaluation. Experiments show that the networks found by our HiNAS achieves highly competitive performance compared with state-of-the-art algorithms, while having fewer parameters and a faster speed.
We conduct comparison experiments to analyse the network architectures found by our NAS algorithm in terms of the internal structure, offering some insights in architectures found by NAS.
1.1 Related Work
CNNs for image denoising. To date, due to the popularity of convolutional neural networks (CNNs), image denoising algorithms have achieved a significant performance boost. Recent network models such as DnCNN  and IrCNN  predict the residue presented in the image instead of the denoised image, showing promising performance. Lately, FFDNet  attempts to address spatially varying noise by appending noise level maps to the input of DnCNN. NLRN  incorporates non-local operations into a recurrent neural network (RNN) for image restoration. N3Net  formulates a differentiable version of nearest neighbor search to further improve DnCNN. DuRN-P  proposes a new style of residual connection, where two residual connections are employed to exploit the potential of paired operations. Some algorithms focus on denoising for real-noisy images. CBDNet  uses a simulated camera pipeline to supplement real training data. Similar work in  proposes a camera simulator that aims to accurately simulate the degradation and noise transformation performed by camera pipelines.
Network architecture search (NAS). NAS aims to design automated approaches for discovering high-performance neural architectures such that the procedure of tedious and heuristic manual design of neural architectures can be eliminated from the deep learning pipeline. Early attempts employ evolutionary algorithms (EAs) for optimizing neural architectures and parameters. The best architecture may be obtained by iteratively mutating a population of candidate architectures . An alternative to EA is to use reinforcement learning (RL) techniques, e.g., policy gradients [48, 37] and Q-learning , to train a recurrent neural network that acts as a meta-controller to generate potential architectures—typically encoded as sequences—by exploring a predefined search space. However, EA and RL based methods are inefficient in search, often requiring a large amount of computations. Speed-up techniques are therefore proposed to remedy this issue. Exemplar works include hyper-networks , network morphism  and shared weights .
In terms of the design of search space and search strategies, our work is most closely related to DARTS , ProxylessNAS  and Auto-Deeplab . DARTS is based on the continuous relaxation of the architecture representation, allowing efficient search of the cell architecture using gradient descent, which has achieved competitive performance. Motivated by this search efficiency, here we also use the gradient based approach as our search strategy. In addition, we employ convolution operations with adaptive receptive field in building our search space. We then extend the search space to include widths for cells by layering multiple candidate paths. Another optimization based NAS approach that has widths included in its search space is ProxylessNAS. However, it is limited to discover sequential structures and chooses kernel widths within manually designed blocks (Inverted Bottlenecks ). By introducing multiple paths of different widths, the search space of our HiNAS resembles Auto-Deeplab. The three major differences are: 1) to retain high resolution feature maps, we do not downsample the feature maps but reply on automatically selected dilated convolutions and deformable convolutions to adapt the receptive field; 2) we share the cell across different paths which leads to significant memory efficiency, only of that is needed by Auto-Deeplab counterparts; 3) to avoid the performance of the selected network degrading after a certain number of epochs (collapse problem), we employ a simple but effective early stopping search strategy. In addition, our HiNAS is proposed for low-level image restoration tasks, the three methods mentioned above are all proposed for high-level image understanding tasks. DARTS  and ProxylessNAS  are proposed for image classification. Auto-Deeplab  finds architectures for semantic segmentation.
Two more relevant works are E-CAE  and FALSR . E-CAE  employs EA to search for an architectures of convolutional autoencoders for image inpainting and denoising. FALSR  is proposed for super resolution tasks. FALSR combines RL and EA and design a hybrid controller as its model generator. Both E-CAE and FALSR require a relatively large amount of computations and takes a large amout of GPU time for searching. Different from E-CAE and FALSR, our HiNAS employs gradient based strategies in searching for architectures for low-level image restoration tasks, probably for the first time, and shares cells across different feature levels in order to save memory. Our method only needs about 4.5 GPU hours to find a high-performing architecture on the BSD500 dataset (see Section 3.5).
2 Our Approach
Following [21, 2], we employ gradient-based architecture search strategies in our HiNAS and we search for a computation cell as the basic block then build the final architecture by stacking the found block with different widths. HiNAS defines a flexible hierarchical search space to design architectures for image denoising. In this section, we first introduce how to search for architectures of cells using continuous relaxation and adaptive search space. Then we explain how to determine the widths via multiple candidate paths and cell sharing. Last, we present our search strategy and our the loss functions.
2.1 Inner Cell Architecture Search
Continuous relaxation. For inner cell architecture search, we employ the continuous relaxation strategy proposed in DARTS . More specifically, we build a supercell that integrates all possible layer types, which is show in the left side of Figure 1. This supercell is a directed acyclic graph containing a sequence of nodes. In Figure 1, we only show three nodes for clear exposition.
We denote the super cell in layer as , which takes outputs of previous cells and the cell before previous cells as inputs and outputs a tensor . Inside , each node takes the two inputs of the current cell and the outputs of all previous nodes as input and outputs a tensor. Taking the th node in as an example, the output of this node is calculated as follows:
where is the input set of node . and are the outputs of cells in layers and , respectively. is the set of possible layer types. Here, to make the search space continuous, we operate each in an continuous relaxation fashion, which is:
where correspond to possible layer types. denotes the weight of operator .
Adaptive search space. Following several recent image restoration networks [19, 32, 15], we do not reduce the spatial resolution of the input. To preserve pixel-level information for low-level image processing, we do not downsample the features but rely on operations with adaptive receptive field such as dilated convolutions and deformable convolutions. In this paper, we pre-define the following 6 types of basic operators:
sep: separable convolution;
dil: convolution with dilation rate of 2;
def: deformable convolution v2 ;
skip: skip connection;
none: no connection and return zero.
Each convolution operation starts with a ReLU activation layer and is followed by a batch normalization layer.
is the concatenation of the outputs of nodes and it can be expressed as:
In summary, the task of cell architecture search is to learn continuous weights , which are updated via gradient descent. After the supercell is trained, for each node, we rank the corresponding inputs according to values, then keep the top two inputs and remove the rest to obtain the compact cell, as shown in the right-side of Figure 1.
2.2 Memory-Efficient Width Search
Multiple candidate paths. Now we have presented the main idea of cell architecture search, which is used to design the specific architectures inside cells. As previously mentioned, the overall network is built by stacking several cells of different widths. To build the overall network, we still need to either heuristically set the width of each cell or search for a proper width for each cell automatically. In conventional CNNs, the change of widths of convolution layers is often related to the change of spatial resolutions. For instance, doubling the widths of following convolution layers after the features are downsampled. In our HiNAS, instead of using downsample layers, we rely on operations with adaptive receptive field such as dilated convolutions and deformable convolutions to adjust the receptive field automatically. Thus the conventional experience of adjusting width no longer applies to our case.
To solve this problem, we employ the flexible hierarchical search space and leave the task of deciding width of each cell to the NAS algorithm itself, making the search space more general. In fact, several NAS algorithms in the literature also search for the outer layer width, mostly for high-level image understanding tasks. For example, FBNet  and MNASNet consider different expansion rates inside their modules to discover compact networks for image classification.
In this section, we introduce the outer layer width search space which determines the widths of cells in different layers. Similarly, we build a supernet that contains several supercells with different widths in each layer. As illustrated in the left-side of Figure 2, the supernet mainly consists of three parts:
1) start part, consisting of input layer and two convolution layer;
2) middle part, containing layers and each layer having three supercells of different widths;
3) end part, concatenating the outputs of , then feeding them to a convolution layer to generate the output.
Our supernet provides three paths of cells with different widths. For each layer, the supernet decides to increase the width by twice, keeping previous width or reducing the width by two. After searching, only one cell at each layer is kept. The continuous relaxation strategy mentioned in the cell architecture search section is reused for inter cell search.
At each layer , there are three cells , and with widths , and , where is the basic width and is set to 10 during search phase. The output feature of each layer is
where is the output of . The channel width of is , where is the number of nodes in the cells.
Cell sharing. Each cell is connected to , and in the previous layer and two layers before. We first process the outputs from those layers with a convolution to form features with width , matching the input of . Then the output for the th cell in layer is computed with
where is the weight of . We combine the three outputs of according to corresponding weights then feed them to as input. Here, features , and come from different levels, but they share the cell during computing .
Note the similarity of this design with Auto-Deeplab, which is used to select feature strides for image segmentation. However, in Auto-Deeplab, the outputs from the three different levels are first processed by separate cells with different sets of weights before summing into the output:
For the hierarchical structure which has three candidate paths, the cell in each candidate path is used once with Eq. (5) and it is used three times with Eq. (6). By sharing the cell , we are able to save the memory consumption by a factor of 3 in the supernet, thus making it possible to use a deeper and wider supernet for more accurate approximations. This also enables us to use larger batch sizes during search, accelerating the search process.
Deriving final architecture. Note that, different from the cell architecture search, we can not simply rank cells of different widths according to values then keep the top one cell. In cell widths search, the channel widths of outputs of different cells in the same layer can be very different. Using the strategy that we have adopted in cell architecture search may lead to the widths of adjacent layers in the final network change drastically, which has a negative impact on the efficiency, as explained in . In cell width search, we view the values as probability, then use the Viterbi decoding algorithm to select the path with the maximum probability as the final result.
2.3 Searching Using Gradient Descent
Optimization function. In terms of the optimization method, our proposed HiNAS belongs to differentiable architecture search. The searching process is the optimization process. For image denoising, the two most widely used evaluation metrics are PSNR and SSIM ; and we design the following loss for optimizing supernet:
Here and denote the input image and corresponding ground-truth. is a loss item that is designed to enforce the visible structure of the result. is the supernet. is structural similarity . is a weighting coefficient and it is empirically set to 0.5 in all of our experiments.
Early stopping search. During optimizing the supernet with gradient descent, we find that the performance of network founded by HiNAS is often observed to collapse when the number of search epochs becomes large. The very recent method of Darts+ , which is concurrent to this work here, presents similar observations. Because of this collapse issue, it is hard to pre-set the number of search epochs. To solve this problem, we employ an early stopping search strategy. Specifically, we split the training set into three disjoint parts: Train W, Train A and Validation V. Sub-datasets W and A are used to optimize the weights of the supernet (kernels in convolution layers) and weights of different layer types and cells of different widths ( and ). During optimizing, we periodically evaluate the performance of the trained supernet on the validation dataset V. We stop the search procedure when the performance of supernet decreases for a pre-determined number of evaluations. Then we choose the supernet which offers the highest PSNR and SSIM scores on validation dataset V as the result of the architecture search. Details are presented in the search settings of Section 3.1.
3.1 Datasets and Implementation Details
Datasets We carry out the deboising experiments on two datasets. The first one is BSD500 . Following [28, 34, 19, 23], we use as the training set the combination of 200 images from the training set and 100 images from the validation set, and test on 200 images from the test set. On this dataset, we generate noisy images by adding white Gaussian noises to clean images with .
The second one is SIM1800, built by ourselves. As the additive white noise models is not able to accurately reproduce the true noise in real world, by using the camera pipeline simulation method proposed in , we build this new denoising dataset SIM1800, which contains 1600 training samples and 212 test samples. Firstly, we use the camera pipeline simulation method to add noises to 25k patches extracted from the MIT-Adobe5k dataset . We then manually pick 1812 patches which have the most realistic visual effects and finally randomly select 1600 patches as the training set and use the rest as the test set.
Search settings. The supernet that we build for image denoising consists of 4 cells and each cell has 5 nodes. we perform architecture search on BSD500 and apply the networks found by HiNAS on both denoising datasets. Specifically, we randomly choose 2% of training samples as the validation set (Validation V). The rest are equally divided into two parts: one part is used to update the kernels of convolution layers (Train W) and the other part is used to optimize the parameters of the neural architecture (Train A).
We train the supernet at most 100 epochs with batch size of 12. We optimize the parameters of kernels and architecture with two optimizers. For learning the kernels of convolution layers, we employ the standard SGD optimizer. The momentum and weight decay are set to 0.9 and 0.0003, respectively. The learning rate decays from 0.025 to 0.001 with the cosine annealing strategy . For learning the parameters of an architecture, we use the Adam optimizer, where both learning rate and weight decay are set to 0.001. In the first 20 epochs, we only update the parameters of kernels, then we start to alternately optimize the kernels of convolution layers and architecture parameters from epoch 21.
During the training process of searching, we randomly crop patches of and feed them to the network. During evaluation, we split each image to some adjacent patches of and then feed them to the network and finally join the corresponding patch results to otain final results of the whole test image. We evaluate the supernet for every epoch.
Training settings We train the network for 600k iterations with the Adam optimizer, where the initial learning rate, batchsize are set to 0.05 and 12, respectively. For data augmentation, we use random crop, random rotations , horizontal and vertical flipping. For random crop, the patches of are randomly cropped from input images.
3.2 Benefits of Searching for the Outer Layer Width
|Models||# parameters (M)||PSNR||SSIM|
In this section, to evaluate the benefits of searching outer layer width, we apply our HiNAS on BSD500 with three different search settings, which are denoted as HiNAS-ws, HiNAS-w40, HiNAS-wm. For HiNAS-ws, both inner cell architectures and out layer width are found by our HiNAS algorithm. For the latter two settings, only the inner cell architectures are found by our algorithm and the outer layer widths are set manually. The basic width of each cell are set to 40 for HiNAS-w40. In HiNAS-wm, we set the basic width of the first cell to 10, then double the basic width cell by cell. The three settings are shown in Figure 4. The comparison results for denoising on BSD500 of are listed in Table 1.
As shown in Table 1, from HiNAS-ws to HiNAS-w40, PSNR and SSIM show slight improvement, 0.01 for PSNR and 0.0003 for SSIM. Meanwhile the corresponding number of parameters is increased by 52%. HiNAS-wm shows the worst performance, and yet it contains the most parameters. With searching for the outer layer width, HiNAS-ws achieves the best trade-off between the number of parameters and accuracy.
3.3 Benefits of Using Loss
Here we analyze how our designed loss item improves image restoration results. We implement two baselines: 1) HiNAS trained with single MSE loss; and 2) HiNAS trained with the combination MSE loss and . Table 5 shows the results of these two methods and that of N3Net on the BSD500 dataset. It is clear that both HiNAS and HiNAS outperform the competitive model, while HiNAS trained with the combination loss shows even better results over HiNAS .
3.4 Architecture Analysis
Now let us analyse the architectures designed by HiNAS. Figures 5 (a) and (b) show the search results in outer network level and the details inside cells, respectively. From Figures 5 (a) and (b), we can see that:
In the denoising network found by our HiNAS, the width of cell that is most close to output layer has the maximum number of channels. This is consist with previous manually designed networks.
Generally speaking, with the same widths, deformable convolution is more flexible and powerful than other convolution operations. Even so, inside cells, instead of connecting all the nodes with the powerful deformable convolution, HiNAS connects different nodes with different types of operators, such as conventional convolution, dilated convolution and skip connection. We believe that these results prove that HiNAS is able to select proper operators.
Separable convolutions are not included in the searched results. We conjecture that this is caused by the fact that we do not limit FLOPS or number of parameters during search. Interestingly, the networks found by our HiNAS still have fewer parameters than other manual models.
|Methods||# parameters (M)||= 30||= 50||= 70||GPU||time cost||search method|
|E-CAE ||1.05||28.23||0.8047||26.17||0.7255||24.83||0.6636||4 Tesla P100||96||EA|
|HiNAS||0.63||29.14||0.8403||26.77||0.7635||25.48||0.7129||1 Tesla V100||16.5||gradient|
|Methods||# parameters (M)||time cost (s)|
From Figure 5 (b), we can see that the networks found by HiNAS consist of many fragmented branches, which might be the main reason why the designed networks have better performance than previous denoising models. As explained in , the fragmentation structure is beneficial for accuracy. Here we verify if HiNAS improves the accuracy by designing a proper architecture or by simply integrating various branch structures and convolution operations. We modify the architecture found by our HiNAS in two different ways and then compare the modified architectures with unmodified architectures.
The first modification is replacing conventional convolutions in the searched architectures with deformable convolutions as shown in Figure 5 (c). As mentioned above, deformable convolution is more flexible than conventional convolution, replacing conventional convolutions with deformable convolutions in theory should improve the capacity of networks. The other modification is to change the connection relationships between nodes inside each cell, as shown in Figure 5 (d), which is aiming to verify if the connection relationship built by our HiNAS is indeed appropriate.
The modification parts are marked in red in Figure 5 (c) and (d). Following the two proposed modifications, we also modify other parts for comparison experiments. However, limited by space, we only show two examples here. The comparison results are listed in Table 3, where the two mentioned modification operations, are denoted as and .
From Table 3, we can see that both modifications reduce the accuracy. Replacing convolution operation reduces the PSNR and SSIM by 0.08 and 0.0005, respectively. Changing connection relationships decreases the PSNR and SSIM to 29.13 and 0.8400, respectively.
From the comparison results, we can draw a conclusion: HiNAS does find a proper structure and select proper convolution operations, instead of simply integrating a complex network with various operations. The fact that a slight perturbation to the found architecture deteriorates the accuracy indicates that the found architecture is indeed a local optimum in the architecture search space.
3.5 Comparisons with Other NAS Methods
Inspired by recent advances in NAS, three NAS methods have been proposed for low-level image restoration tasks [33, 4, 22]. E-CAE  is proposed for image inpainting and denoising. FALSR  is proposed for super resolution. EvoNet  searches for networks for medical image denoising. All three methods are based on EA and require a large amount of compuational resources and are GPU time hungry. By using four P100 GPUs, E-CAE takes four days (384 GPU hours) to execute the evolutionary algorithm and fine-tune the best model for denoising on BSD500. FALSR takes about 3 days on 8 Tesla-V100 GPUs (576 GPU hours) to find the best architecture. EvoNet uses 4 Geforce TITAN GPUs and takes 135 hours for finding the best gene. Here we mainly focus on comparing our HiNAS with E-CAE, because both them are proposed for searching for architectures for the task of denoising on BSD500. Table 4 shows the details.
Compared with E-CAE , FALSR  and EvoNet , our HiNAS is much faster in searching. By using a single Tesla V100, HiNAS takes about 4.5 hours in searching and 12 hours for training the network found by our algorithm. The fast search speed of our HiNAS benefits from the following three advantages.
HiNAS uses a gradient based search strategy. EA based NAS methods generally need to train a large number of children networks (genes) to update their populations. For instance, FALSR trained about 10k models during its searching process. In sharp contrast, our HiNAS only needs to train one supernet in the search stage.
In searching for the outer layer width, we share cells across different feature levels, saving memory consumption in the supernet. As a result, we can use larger batch sizes for training the supernet, which further speeds up search.
By using a simple early-stopping search strategy, HiNAS further saves 0.5 to 1.5 hours in the search stage.
3.6 Comparisons with State-of-the-art
Now we compare the HiNAS designed networks with a number of recent methods and use PSNR and SSIM to quantitatively measure the restoration performance of those methods. The comparison results on BSD500 and SIM1800 are listed in Table 5 and Table 6, respectively. Figures 6 and 7 show the visualization.
Table 5 shows that N3Net and HiNAS beat other models by a clear margin. Our proposed HiNAS achieves the best performance when is set to 50 and 70. When the noise level is set to 30, the SSIM of NLRN is slightly higher (0.002) than that of our HiNAS, but the PSNR of NLRN is much lower (nearly 1dB) than that of HiNAS.
Overall our HiNAS achieves better performance than others. In addition, compared with the second best model N3Net, the network designed by HiNAS has fewer parameters and is faster in inference. As listed in Table 5, the HiNAS designed network has 0.63M parameters, which is 92.65% that of N3Net and 60% that of E-CAE. Compared with N3Net, the HiNAS designed network reduces the inference time on the test set of BSD500 by 31.26%.
We compare the network designed by HiNAS with NLRN and N3Net on SIM1800. Table 6 lists the results, from which we can see that the SSIM of the HiNAS desgined network is much higher than that of NLRN and N3Net. However, PSNR of the HiNAS designed network is slightly lower than that of NLRN and N3Net. In summary, the performance of the HiNAS designed network is competitive with that of NLRN and N3Net on SIM1800. Figure 7 shows a visual comparison.
Additional experiments We apply the proposed HiNAS on a challenging de-raining dataset Rain800. The supernet that we build for image de-raining contains 3 cells and each cell is made up of 4 nodes. Search and training setting are consistent with that of the denoising experiments, except that we use random crop and horizontal flipping for augmentation. The results are listed in Table 3 and shown in Figure 5. As shown in Table 3, the de-raining network designed by HiNAS achieves much better performance than others. Comparing RESCAN to the network designed by HiNAS, PSNR and SSIM are improved by 2.22 and 0.0275, respectively. In addition, the inference speed of HiNAS designed de-raining network is 2.03 that of RESCAN.
In this work, we have proposed HiNAS, an memory-efficient hierarchical architecture search algorithm for the low-level image restoration task image denoising. HiNAS adopts differentiable architecture search algorithms and a cell sharing strategy. It is both memory and computation efficient, taking only about 4.5 hours to search using a single GPU. In addition, a simple but effictive early stopping strategy is used to avoid the NAS collapse problem. Our proposed HiNAS achieves highly competitive or better performance compared with previous state-of-the-art methods with fewer parameters and a faster inference speed. We believe that the proposed method can be applied to many other low-level image processing tasks.
Acknowledgments C. Shen’s participation was in part supported by the ARC Grant “Deep learning that scales”.
- thanks: This work was done when H. Zhang was visiting The University of Adelaide. Correspondence: C. Shen ().
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