Learned transform and compressive sensing for video coding

In a video encoder, a method, comprising:

• encoding a block in a picture based on an adaptive transform that is a sparsifying transform determined from a training set,
• wherein the encoding includes reconstructing the block in a pixel domain to obtain a reconstructed block
• wherein the reconstructed block is determined based on the adaptive transform,
• wherein the adaptive transform is determined based on a minimization based on a variable η, a matrix S that represents a matrix of coefficient vectors, and a matrix X that is composed of training data, and a matrix Φ that is an incoherent sensing matrix, and
• wherein the variable η is tuned adaptively with a quantization parameter.

An apparatus, comprising:

• a video decoder for decoding block in a picture based on an adaptive transform that is a sparsifying transform determined from a training set or a bit stream,
• wherein the video decoder is configured to reconstruct the block in a pixel domain to obtain a reconstructed block,
• wherein the reconstructed block is determined based on the adaptive transform,
• wherein the adaptive transform is determined based on a minimization based on a variable η, a matrix S that represents a matrix of coefficient vectors, and a matrix X that is composed of training data, and a matrix Φ that is an incoherent sensing matrix, and
• wherein the variable η is tuned adaptively with a quantization parameter.

In a video decoder, a method, comprising:

• decoding an image block in a picture from a bitstream based on an adaptive transform that is a sparsifying transform determined from a training set or a bit stream,
• wherein the decoding includes reconstructing the block in a pixel domain to obtain a reconstructed block,
• wherein the reconstructed block is determined based on the adaptive transform,
• wherein the adaptive transform is determined based on a minimization based on a variable η, a matrix S that represents a matrix of coefficient vectors, and a matrix X that is composed of training data, and a matrix Φ that is an incoherent sensing matrix, and
• wherein the variable η is tuned adaptively with a quantization parameter.

A non-transitory computer readable storage media having video signal data encoded thereupon, comprising:

• a block in a picture encoded based on an adaptive transform that is a sparsifying transform determined from a training data set,
• wherein the block was encoded by reconstructing the block in a pixel domain to obtain a reconstructed block,
• wherein the reconstructed block is determined based on the adaptive transform,
• wherein the adaptive transform is determined based on a minimization based on a variable η, a matrix S that represents a matrix of coefficient vectors, and a matrix X that is composed of training data, and a matrix Φ that is an incoherent sensing matrix, and
• wherein the variable η is tuned adaptively with a quantization parameter.