Convolutional Sparse Coding

Synonyms

Convolutional dictionary learning; Convolutional sparse representations

Related Concepts

• Dictionary Learning

• Sparse Coding

• Sparse Representation Learning

Definition

Convolutional sparse coding is the method of learning sparse representations {x_j} of a signal s, which is reconstructed from the sparse representations’ convolution with a set of linear filters{d_j} (also known as templates or dictionaries):

$$\displaystyle \begin{aligned} \boldsymbol{s}= \sum_{j} \boldsymbol{d}_j \ast \boldsymbol{x}_j \end{aligned} $$

(1)

The signal can be an image, an audio clip, a sequence of words, or even a video clip.

Background

Representation learning forms a cornerstone of modern machine learning. Representing the data in the relevant feature space is critical to obtaining good performance in challenging machine learning tasks in speech, computer vision, and natural language processing.

Sparse Coding

Sparse coding is one of the most widely used models for inverse problems in signal...