Project to implement sparse codes for natural images across multiple scales of laplacian pyramid. The goal is that the network should be able to encode the scale structure of natural scenes in a more efficient manner. Applications in efficient coding, classification, denoising and occlusion.

* To Do
x Done

[*] - Add a preprocesssing remove 8x8 patch
[*] - Fix generating matrix gaussian std. dev.
[*] - Fix update G^T scale
[*] - Fix generating matrix
[*] - Non normalize
[*] - Display coefficients topographic\Animate laplacian
[*] - lambda small at low frequency, large at low frequency
[*] - look at coefficient variance at different levels
[*] - synthesis (different lambdas)
[*] - weighted norm l1/l2 - pairwise (across scale l1/l2 norm)
[*] - fix alignment of laplacian generative matrix (ln 105 in laplacian_pyramid - some offset related to scale)?

For Redwood Presentation:
[*] - Project filters back to image domain
[*] - Look at variance on each scale
[*] - Animated GIF of image reconstruction
[*] - Sparsity vs MSE of conv vs non conv
[*] - Occlusion model
[*] - Compare convolution model to non-convolution model

For NIPS paper:
[*] - Scale to 256x256
	[*] - Change sparse Phi to GPU 
		[*] - Rewrite update with GPU kernels
		[*] - Gram matrix computation is different
		[x] - Replace G with upscale and blur
	[*] - Use sparse matrix multiply for inference
[*] - Non-convolutional and multiscale fields of experts
[*] - Occlusion with binary mask
[*] - OC convolution vs tiled representation (where can you add parameters)

[*] - Optimal image for deep net
Paper
[*] - Replace G[s] with blur (1D convolution) and upsample 
[*] - MRI
[*] - Visualizing deep nets
[*] - Play around with filter stride
[*] - Do smarter inference (i.e. only look at local connections). Band matrix multiply
[*] - Train a convolutional laplacian pyramid
[*] - Try out the non convolutional model on a different test set
[x] - Image reconstruction with l1 norm and mse
[x] - Entropy for a fixed SNR
[x] - julien mairal thesis 
[x] - state of the art in image denoising
[x] - read portia and simoncelli, zetczshe, lyu+simoncelli, bethge

To Do: 
[x] - Solve proximal
[x] - Do GPU
[x] - IHT and denoising (better results?)
[x] - Compare IHT and sparse coding multiscale to miki elad denoising (learn better basis functions)
[x] - FISTA on GPU
[x] - normalize basis functions based on unit norm
[*] - Instead normalize based on scale max(1)
[*] - Fix gain on laplacian generative model - scale DC gain to 4 (4 pixels interpolating at each level)
[*] - Implement Nesterov Momentum -- Tried, not really beneficial. 
[x] - Sparsity level at different levels
[x] - Preprocess image by LPF top octave and downsamplel
[x] - Use smaller filter size - derive frequency response of binomial filter
[*] - Compare joint training with learning rates of the same values

Fix:
[x] - Clean up the display
[x] - Clean up Preprocess

To Do:
[x] - Value for lambda given variance and value of coefficients
[x] - SNR reconstruction plots, calculation mse: average over pixes, calculation: SNR: 10 log(inverse of MSE/(pixel variance -- sum square of pixel values))
[x] - Make pretty denoising plots

[x] - Set 0 level of display
[x] - Initialization - overcompleteness
[x] - Initialization - convolutional
[x] - Update - overcompleteness
[x] - Update - convolutional

Dec 11 
[x] Reshape takes O(n^2) time. Use sparse efficient reshape
[x] Use zero padding on all images arrays
[x] Look into using pysparse module instead of scipy.sparse

Nov 21 - Meeting
[*] - Sparsity, recon on old model
[x] - Vanhateran 100,000 patches
[*] - Fit gabors and show tiling with bars 
[*] - Sparsity vs mse
[*] - spatial -> frequency tiling
[*] - Pick reconstruction dB
[*] - Running time of FISTA vs LCA

Nov 21 - Meeting Critical:
[*] - Redo LCA using laplacian generative model
[*]- Redo laplacian pyramid using laplacian pyramid generative model
||X-G_0*Phi_0*a_0||_2^2 + ||a_0||_1

Nov 15 - Meeting with Bruno
[*] - Use more training images (~10,000) 
[*] - Rescale levels of Laplacian Pyramid

Critical
[*] - Use own code to generate pyramid

[*] - Fix the coupling between basis functions on different levels
[*] - FISTA implementation
[*] - Create script for example image reconstruction
[*] - Unwhitened natural images on laplacian pyramid
[*] - Adjust weight on reconstruction error based on level of Laplacian pyramid:
	||recon||/sigma^2 + sparsity == ||recon|| + lambda * sparsity
[x] - Experiment with gaussian std. dev. of kernel. Read Simoncelli multiscale paper

Old
[*] - In reconstruction currently modulo the image_side size. Maybe fix so that basis functions across scales aren't grouped together?
[*] - Generalize reconstruction() for multiple images
[*] - Overcomplete representations as that will lead to basis functions on different levels
[*] - Write down equation for reconstruction of image from gabor basis
[*] - Don't resize images at each level
[*] - Fix how I'm expanding each level to image size
	[*] - Affects how I calculate residuals
	[*] - Currently we fix each basis function to be 8 x 8 x S. We do not decrease the size of the basis functions at each level

Interesting
[x] - Object localization?
[*] - Sparse matrix generative model


Files
berkeley_32_3_20.npy 20 Images from Berkeley Dataset. 32*32 with a 3 scale Laplacian Pyramid Representation