Sigma Delta quantization for images
View Patent ↗A technique is presented for quantizing pixels of an image using Sigma Delta quantization. In one aspect, pixel values for an image are segmented into columns of pixel values; and for each column in the matrix, pixel values of a given column are quantized using sigma delta modulation. The pixel values in a given column are preferably quantized as a whole, thereby minimizing accumulated quantization error from a starting pixel value in the given column to a current pixel value in the given column. In another aspect, the pixels of an image are quantized using a 2D generalization of Sigma Delta modulation.
1. A method for quantizing pixels of an image, comprising:
receiving, by a sequencing circuit, pixel values for an image captured by a camera, where the pixel values are arranged in a matrix;
grouping, by the sequencing circuit, the pixel values of the matrix into columns of pixel values;
for each column in the matrix, quantizing, by an analog to digital converter, pixel values of a given column as a whole using sigma delta modulation thereby minimizing accumulated quantization error for the given column from a starting pixel value in the given column to a current pixel value in the given column; and
reconstructing a final image from the quantized pixel values of the matrix using a decoder, where the decoder is configured to minimize an image norm subject to a quantization constraint and the quantization constraint is defined by a finite integration operator applied to a quantization error with an L-infinite norm bounded by half of the quantization step-size, wherein the quantization error is a vector such that each element of the vector contains a quantization error for a given pixel in the matrix.
2. The method of claim 1 further comprises quantizing two or more columns of pixel values from the matrix in series using sigma delta modulation.
3. The method of claim 1 further comprises assembling quantized values for each column into a rectangular array and storing the rectangular array as a final image in a non-transitory computer-readable medium.
4. The method of claim 1 wherein the image norm is further defined as a total variation norm.
5. An imaging system, comprising:
a camera configured to capture an image of a scene, where the image is represented by pixel values arranged in a matrix;
a sequencing circuit configured to receive the image from the camera and operates to grouping the pixel values of the matrix into columns of pixel values; and
an analog to digital converter interfaced with the sequencing circuit and, for each column in the matrix, quantizes pixel values of a given column as a whole using sigma delta modulation, thereby minimizing accumulated quantization error for the given column from a starting pixel value in the given column to a current pixel value in the given column; and
a decoder configured to receive the quantized pixel values of the matrix and reconstructing a final image from the quantized pixel values of the matrix, where the decoder minimizes an image norm subject to a quantization constraint and the quantization constraint is defined by a finite integration operator applied to a quantization error with an L-infinite norm bounded by half of the quantization step-size, and the quantization error is a vector such that each element of the vector contains a quantization error for a given pixel in the matrix.
6. A method for quantizing pixels of an image, comprising:
receiving, by a sequencing circuit, pixel values for an image captured by a camera, where the pixel values are arranged in a matrix;
grouping, by the sequencing circuit, the pixel values of the matrix into columns of pixel values;
for each column in the matrix, quantizing, by an analog to digital converter, pixel values of a given column as a whole using sigma delta modulation thereby minimizing accumulated quantization error for the given column from a starting pixel value in the given column to a current pixel value in the given column; and
reconstructing, by a decoder, a final image from the quantized pixel values of the matrix while minimizing a norm subject to a quantization constraint, where the quantization constraint is defined by a finite integration operator applied to a quantization error with an L-infinite norm bounded by half of the quantization step-size, and the quantization error is a vector such that each element of the vector contains a quantization error for a given pixel in the matrix.
7. The method of claim 6 further comprises quantizing two or more columns of pixel values from the matrix in parallel using sigma delta modulation.
8. The method of claim 6 further comprises quantizing two or more columns of pixel values from the matrix in series using sigma delta modulation.
9. The method of claim 6 further comprises assembling quantized values for each column into a rectangular array and storing the rectangular array as a final image in a non-transitory computer-readable medium.
10. The method of claim 6 wherein the norm is further defined as a total variation norm.