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ALISTA: Analytic Weights Are As Good As Learned Weights in LISTA

This repository is for Analytic-LISTA networks proposed in the following paper:

Jialin Liu*, Xiaohan Chen*, Zhangyang Wang and Wotao Yin "ALISTA: Analytic Weights Are As Good As Learned Weights in LISTA", accepted at ICLR 2019. The pdf can be found here..

*: These authors contributed equally and are listed alphabetically.

The code is tested in Linux environment (Python: 3.5.2, Tensorflow: 1.12.0, CUDA9.0) with Nvidia GTX 1080Ti GPU.


Deep neural networks based on unfolding an iterative algorithm, for example, LISTA (learned iterative shrinkage thresholding algorithm), have been an empirical success for sparse signal recovery. The weights of these neural networks are currently determined by data-driven “black-box” training. In this work, we propose Analytic LISTA (ALISTA), where the weight matrix in LISTA is computed as the solution to a data-free optimization problem, leaving only the stepsize and threshold parameters to data-driven learning. This significantly simplifies the training. Specifically, the data-free optimization problem is based on coherence minimization. We show our ALISTA retains the optimal linear convergence proved in (Chen et al., 2018) and has a performance comparable to LISTA. Furthermore, we extend ALISTA to convolutional linear operators, again determined in a data-free manner. We also propose a feed-forward framework that combines the data-free optimization and ALISTA networks from end to end, one that can be jointly trained to gain robustness to small perturbations in the encoding model.

Run the codes

Generate problem files

To run most of experiments in this repository, you need to first generate an instance of Problem or ProblemConv class, which you can find in utils/ or utils/ file.

Run the following command to generate a random measurement matrix:

python3 utils/ --M 250 --N 500 \
    --pnz 0.1 --SNR inf --con_num 0.0 --column_normalized True

Explation for the options:

  • --M: the dimension of measurements.
  • --N: the dimension of sparse signals.
  • --pnz: the approximate of non-zero elements in sparse signals.
  • --SNR: the signal-to-noise ratio in dB unit in the measurements. inf means noiseless setting.
  • --con_num: the condition number. 0.0 (default) means the condition number will not be changed.
  • --column_normalized: whether normalize the columns of the measurement matrix to unit l-2 norm.

The generated will be saved to the experiments/m250_n500_k0.0_p0.1_s40/prob.npz. If you want to generate a problem from an existing measurement matrix, which should be saved in Numpy npy file format, use --load_A option with the path to the matrix file. In this case, options --M and --N will be overwriiten by the shape of loaded matrix.

Baseline: LISTA-CPSS

Use the baseline model LISTA-CPSS in this paper to basicly explain how to train and test models. To train or test a LISTA-CPSS model, use the following command:

python3 --task_type sc -g 0 [-t] \
    --M 250 --N 500 --pnz 0.1 --SNR inf --con_num 0 --column_normalized True \
    --net LISTA_cpss -T 16 -p 1.2 -maxp 13 \
    --scope LISTA_cpss --exp_id 0

Explanation for the options (all optinos are parsed in

  • --task_type: the task on which you will train/test your model. Possible values are:
    • sc standing for normal simulated sparse coding algorithm;
    • cs for natural image compressive sensing;
    • denoise for natural image denoising using convolutional LISTA;
    • encoder for encoder pre-training; and
    • robust for robustness training.
  • -g/--gpu: the id of GPU used. GPU 0 will be used by default.
  • -t/--test option indicates training or testing mode. Use this option for testing.
  • -n/--net: specifies the network to use.
  • -T: the number of layers.
  • -p/--percent: the percentage of entries to be added to the support in each layer.
  • -maxp/--max_percent: maximum percentage of entries to be selected.
  • --scope: the name of variable scope of model variables in TensorFlow.
  • --exp_id: experiment id, used to differentiate experiments with the same setting.


To train or test a TiLISTA (Tied-LISTA) network, run the following command:

python3 --task_type sc -g 0 [-t] \
    --M 250 --N 500 --pnz 0.1 --SNR inf --con_num 0 --column_normalized True \
    --net TiLISTA -T 16 -p 1.2 -maxp 13 \
    --scope TiLISTA --exp_id 0


Solve analytic weight from measurement matrix

Use MatLab script matlabs/CalculateW.m to solve an analytic weight matrix from an existing measurement matrix, which should be saved as a MatLab mat file with key word D for the matrix. We provide an example in data/D.mat, which is the same matrix as in experiments/m250_n500_k0.0_p0.1_sinf/prob.npz. Use matlabs/CalculateW_conv.m for convolutional dictionaries. We provide a pre-solved weight saved as data/W.npy.

ALISTA with analytic weight

python3 --task_type sc -g 0 [-t] \
    --M 250 --N 500 --pnz 0.1 --SNR inf --con_num 0 --column_normalized True \
    --net ALISTA -T 16 -p 1.2 -maxp 13 -W ./data/W.npy \
    --better_wait 2000 \
    --scope ALISTA --exp_id 0

Explanation for options:

  • -W: path to the specified weight matrix.
  • --better_wait: maximum waiting time for a better validation accuracy before going to the next training stage. ALISTA model has 2T parameters, thus having a very stabilized training process. Therefore, we can use a smaller waiting time than LISTA-CPSS (use --better_wait 5000 by default).


To train a robust ALISTA model, you need 3 steps:

  1. Pre-train a encoder.
  2. Pre-train a ALISTA decoder. We can use the ALISTA modeled trained in the above section.
  3. Jointly train the encoder and the decoder.

Pre-train encoders

python3 --task_type encoder -g 0 \
    --M 250 --N 500 --pnz 0.1 --SNR inf --con_num 0 --column_normalized True \
    --net AtoW_grad --eT 4 --Binit default --eta 1e-3 --loss rel2 \
    --Abs 16 --encoder_psigma 1e-2 --encoder_pre_lr 1e-4 \
    --scope AtoW --exp_id 0

Explanation for the options:

  • --net AtoW_grad: the encoding model unfoled from projected gradient descent.
  • --eT: the number of layers in the encoder.
  • --Binit: use the default method to initialize weights in the encoder. You can use random initialization by specifying normal or uniform here.
  • --eta: the initial step size in the projected gradient descent.
  • --loss: the objective function in the original optimization, and the cost function used to train the encoder. rel2 means reweighted l2.
  • --Abs: the batch size to sample perturbed matrices.
  • --encoder_psigma: the noise level to perturb the measurement matrix.
  • --encoder_pre_lr: the initial learning rate for pre-training the encoder.

Jointly train encoder and decoder

python3 --task_type robust -g 0 [-t] \
    --M 250 --N 500 --pnz 0.1 --SNR inf --con_num 0 --column_normalized True \
    --net robust_ALISTA \
    --eT 4 --Binit default --eta 1e-3 --loss rel2 --encoder_scope AtoW \
    --encoder_psigma 1e-2 --encoder_pre_lr 1e-4 --encoder_id 0 \
    --dT 16 --lam 0.4 -p 1.2 -maxp 13 -W .data/W.npy \
    --decoder_scope ALISTA --decoder_id 0 \
    --psigma_max 2e-2 --psteps 5 --msigma 0.0 \
    --encoder_lr 1e-9 --decoder_lr 1e-4 \
    --Abs 4 --xbs 16 --maxit 50000 --exp_id 0

Explanation for the options:

  • --dT: the number of layers in the decoder.
  • --psigma_max: the maximum level of perturbations during the joint training.
  • --psteps: the number of steps of the curriculum training where we gradually increase the level of perturbations till psigma_max.
  • --msigma: the level of measurement noises during the joint training.
  • --xbs: the batch size used to generate sparse signals for each perturbed measurement matrix. The total number of measurement-signal pairs in a batch is Abs times xbs.
  • --maxit: the maximum number of training steps for each curriculum training stage in the whole training process.


Use the above command with -t/--t option to test. For testing we genereate a sample of perturbed measurement matrices, which you can download using this Dropbox link. The original measurement matrix used to generate this file is the same as in experiments/m250_n500_k0.0_p0.1_sinf/prob.npz.

Data augmented decoders

To train or test a data-augmented decoding model, run the following command (use TiLISTA for example):

python3 --task_type robust -g 0 [-t] \
    --M 250 --N 500 --pnz 0.1 --SNR inf --con_num 0 --column_normalized True \
    --net TiLISTA -T 16 --lam 0.4 -p 1.2 -maxp 13 \
    --psigma_max 2e-2 --psteps 5 --msigma 0.0 \
    --decoder_lr 1e-4 --Abs 4 --xbs 16 --maxit 50000 \
    --scope TiLISTA --exp_id 0

Convolutional LISTA for natural image denoising

  1. Download BSD500 dataset. Split into train, validation and test sets as you wish.
  2. Genereate the tfrecords using:
    python3 utils/ --task_type denoise \
        --dataset_dir /path/to/your/[train,val,test]/folder \
        --out_dir path/to/the/folder/to/store/tfrecords \
        --out_file [train,val,test].tfrecords \
        --suffix jpg
  3. Learn a convolutional dictionary from the BSD500 dataset using the algorithm in the paper First- and Second-Order Methods for Online Convolutional Dictionary Learning. Or use the dictionary proveided in data/D3_M100_lam0.05.mat.
  4. Generate a problem file using the learned dictionary and the following command:
    python3 utils/ --conv_d 3 --conv_m 100 --conv_lam 0.05 \
        --load_dict ./data/D3_M100_lam0.05.mat
    where --conv_d is the size of filters in the dictionary, --conv_m is the number of filters, --conv_lam is the parameter used in convolutional dictionary learning algorithm, and --load_dict specifies the dictionary to be loaded and saved. The generated problem file will be saved to experiments/denoise_d3_m100_lam0.05/prob.npz.
  5. Train and test the convolutional denoising model (use Conv-TiLISTA as an example):
    python3 --task_type denoise -g 0 [-t] \
        --net TiLISTA -T 5 --lam 0.1 --conv_alpha 0.1 \
        --sigma 20 --height_crop 321 --width_crop 321 \
        --num_epochs -1 --tbs 4 --vbs 16 \
        --data_folder data/denoise_tfrecords
        --train_file training_tfrecords_filename \
        --val_file validation_tfrecords_filename
    Explanation for the options:
    • --conv_alpha: the initial step size in learned convolutional model.
    • --sigma: the noise level in the images.
    • --height_crop and --width_crop: size of cropped images in training.
    • --num_epochs: the number of epochs to train over the BSD500 training set. The default -1 value means infinite nubmer of opochs. The training will be ended as in sc task.
    • --tbs and --vbs: training and validation batch sizes.
    • --data_folder: the path to the folder that holds the tfrecords files.

Cite this work

If you find our code helpful in your resarch or work, please cite our paper.

title={{ALISTA}: Analytic Weights Are As Good As Learned Weights in {LISTA}},
author={Jialin Liu and Xiaohan Chen and Zhangyang Wang and Wotao Yin},
booktitle={International Conference on Learning Representations},


[ICLR 2019] "ALISTA: Analytic Weights Are As Good As Learned Weights in LISTA", by Jialin Liu*, Xiaohan Chen*, Zhangyang Wang and Wotao Yin.








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