Body: <p>I have a deep learning network that outputs grayscale image reconstructions. In addition to good reconstruction performance (measured through mean squared error or some other measure like psnr), I want to encourage these outputs to be sparse through a regularization term in the loss function.</p>
  <p>One way to do this is to add an L1 regularization term that penalizes the sum of the absolute value of pixel intensities. While this is a good start, is there any penalization that take adjacency and spatial contiguity into account? It doesn't have to be a commonly used constraint/regularization term, but even potential concepts or papers that go in this direction would be extremely helpful. In natural images, sparse pixels tend to form regions or patches as opposed to being dispersed or scattered. Are there ways to encourage regions of contiguous pixels to be sparse as opposed to individual pixels?</p>
  
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2020-09-18T02:04:57.503Z
Comments.Text: @DuttaA Interesting idea! Do you have any examples or links that provide more info? Also, is this similar to total variation regularization (which minimizes differences in adjacent pixels)?
Comments.UserDisplayName: Jane Sully
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2020-09-18T09:41:09.467Z
Comments.Text: Does it matter which pixels (or regions) become zero or can they be in random positions? What are you trying to achieve ultimately, i.e. what kind of images are you trying to generate (or reconstruct)? Also, when you say "sparse", do you mean that the pixels will be zero (black)?
Comments.UserDisplayName: nbro
Tags: <deep-learning><objective-functions><image-processing><autoencoders><regularization>
Title: Enforcing sparsity constraints that make use of spatial contiguity
UserDisplayName: Jane Sully
ThreadText: # Enforcing sparsity constraints that make use of spatial contiguity
  
  (Asked by: username_0 on 2020-09-17)
  
  I have a deep learning network that outputs grayscale image reconstructions. In addition to good reconstruction performance (measured through mean squared error or some other measure like psnr), I want to encourage these outputs to be sparse through a regularization term in the loss function.
  
  One way to do this is to add an L1 regularization term that penalizes the sum of the absolute value of pixel intensities. While this is a good start, is there any penalization that take adjacency and spatial contiguity into account? It doesn't have to be a commonly used constraint/regularization term, but even potential concepts or papers that go in this direction would be extremely helpful. In natural images, sparse pixels tend to form regions or patches as opposed to being dispersed or scattered. Are there ways to encourage regions of contiguous pixels to be sparse as opposed to individual pixels?
  
  **Tags:** deep-learning, objective-functions, image-processing, autoencoders, regularization
  > **Comments:**
  > **username_0**: @DuttaA Interesting idea! Do you have any examples or links that provide more info? Also, is this similar to total variation regularization (which minimizes differences in adjacent pixels)?  
  > **username_1**: Does it matter which pixels (or regions) become zero or can they be in random positions? What are you trying to achieve ultimately, i.e. what kind of images are you trying to generate (or reconstruct)? Also, when you say "sparse", do you mean that the pixels will be zero (black)?  
  
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  ## 0 answers
  
  