psnr

Peak signal-to-noise ratio (PSNR)

Syntax

peaksnr = psnr(A,ref)

peaksnr = psnr(A,ref,peakval)

peaksnr = psnr(___,'DataFormat',dataFormat)

[peaksnr,snr]
= psnr(___)

Description

peaksnr = psnr(A,ref) calculates the peak signal-to-noise ratio (PSNR) for the image A, with the image ref as the reference. A greater PSNR value indicates better image quality.

example

peaksnr = psnr(A,ref,peakval) calculates the PSNR of image A using the peak signal value peakval.

peaksnr = psnr(___,'DataFormat',dataFormat) also specifies the dimension labels, dataFormat, of unformatted image data. Use this syntax to return a separate PSNR for each element along a batch dimension.

example

[peaksnr,snr] = psnr(___) also returns the simple signal-to-noise ratio, snr.

example

Examples

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Calculate PSNR for Noisy Image Given Original Image as Reference

Open Live Script

Read image and create a copy with added noise. The original image is the reference image.

ref = imread('pout.tif');
A = imnoise(ref,'salt & pepper', 0.02);

Calculate the PSNR.

[peaksnr, snr] = psnr(A, ref);
  
fprintf('\n The Peak-SNR value is %0.4f', peaksnr);

 The Peak-SNR value is 22.6437

fprintf('\n The SNR value is %0.4f \n', snr);

 The SNR value is 15.5524

Calculate PSNR for `dlarray` Input

Open Live Script

Read an image into the workspace, then create an unformatted dlarray object with the image data.

ref = imread("strawberries.jpg");
ref = im2single(ref);
dlref = dlarray(ref);

Add salt and pepper noise to the image, then create an unformatted dlarray object with the noisy image data.

noisy = imnoise(ref,'salt & pepper');
dlnoisy = dlarray(noisy);

Calculate the peak SNR and SNR of the noisy data with respect to the original data.

[peaksnr,snr] = psnr(dlnoisy,dlref)

peaksnr = 
  1x1 single dlarray

   17.5941

snr = 
  1x1 single dlarray

   11.1265

Calculate PSNR of Images in Image Sequence

Open Live Script

Read a reference image into the workspace.

ref = imread("office_1.jpg");

Preallocate two arrays that store a sequence of six images of the size of the reference image.

numFrames = 6;
imsOriginal = zeros([size(ref) numFrames],class(ref));
imsNoisy = zeros([size(ref) numFrames],class(ref));

Read and add images to the preallocated arrays. One array stores the original image data. The second array stores the image data with added salt and pepper noise.

for p = 1:numFrames
    filename = strcat("office_",num2str(p),".jpg");
    im = imread(filename);
    imsOriginal(:,:,:,p) = im;
    imsNoisy(:,:,:,p) = imnoise(im,"salt & pepper");
end

Display the image sequences in a montage. The first row shows the sequence with original image data. The second row shows the sequence with noisy image data.

montage(cat(4,imsOriginal,imsNoisy),"Size",[2 numFrames])

Figure contains an axes object. The hidden axes object contains an object of type image.

Calculate the PSNR of each noisy image with respect to the corresponding pristine image by specifying the data format of the input arrays as "SSCB" (spatial, spatial, channel, batch).

peak_psnrs = psnr(imsNoisy,imsOriginal,"DataFormat","SSCB");
peak_psnrs = squeeze(peak_psnrs)

peak_psnrs = 6×1

   16.3560
   16.9698
   17.8079
   18.1843
   18.0656
   17.1682

Input Arguments

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`A` — Image to be analyzed
numeric array | `dlarray` object

Image to be analyzed, specified as a numeric array of any dimension or a dlarray (Deep Learning Toolbox) object.

Data Types: single | double | int16 | uint8 | uint16

`ref` — Reference image
numeric matrix | `dlarray` object

Reference image, specified as a numeric array or a dlarray (Deep Learning Toolbox) object. The reference image has the same size and data type as image A.

Data Types: single | double | int16 | uint8 | uint16

`peakval` — Peak signal level
nonnegative number

Peak signal level, specified as a nonnegative number. If not specified, the default value for peakval depends on the class of A and ref.

If the images are of data type double or single, then psnr assumes that image data is in the range [0, 1]. The default value of peakval is 1.
If the images are of integer data types, then the default value of peakval is the largest value allowed by the range of the class. For uint8 data, the default value of peakval is 255. For uint16 or int16, the default is 65535.

`dataFormat` — Dimension labels
string scalar | character vector

Dimension labels of the input images A and ref, specified as a string scalar or character vector. Each character in dataFormat must be one of these labels:

S — Spatial
C — Channel
B — Batch observations

The format cannot include more than one channel label or batch label. Do not specify the 'dataFormat' argument when the input images are formatted dlarray objects.

Example: 'SSC' indicates that the array has two spatial dimensions and one channel dimension, appropriate for 2-D RGB image data.

Example: 'SSCB' indicates that the array has two spatial dimensions, one channel dimension, and one batch dimension, appropriate for a sequence of 2-D RGB image data.

Output Arguments

collapse all

`peaksnr` — PSNR
numeric scalar | numeric array | `dlarray` object

PSNR in decibels, returned as one of these values.

Input Image Type	PSNR Value
Unformatted numeric arrays Formatted numeric arrays without a batch (`'B'`) dimension	Numeric scalar with a single PSNR measurement.
Unformatted `dlarray` (Deep Learning Toolbox) objects	1-by-1 `dlarray` object with a single PSNR measurement.
Numeric arrays with a batch dimension specified using the `dataFormat` argument	Numeric array of the same dimensionality as the input images. The spatial and channel dimensions of `peaksnr` are singleton dimensions. There is one PSNR measurement for each element along the batch dimension.
Formatted `dlarray` objects with a batch dimension Unformatted `dlarray` objects with a batch dimension specified using the `dataFormat` argument	`dlarray` object of the same dimensionality as the input images. The spatial and channel dimensions of `peaksnr` are singleton dimensions. There is one PSNR measurement for each element along the batch dimension.

If A and ref have data type single, then peaksnr has data type single. Otherwise, peaksnr has data type double.

`snr` — Signal-to-noise ratio
numeric scalar | numeric array | `dlarray` object

Signal-to-noise ratio in decibels, returned as one of these values.

Input Image Type	PSNR Value
Unformatted numeric arrays Formatted numeric arrays without a batch (`'B'`) dimension	Numeric scalar with a single SNR measurement.
Unformatted `dlarray` (Deep Learning Toolbox) objects	1-by-1 `dlarray` object with a single SNR measurement.
Numeric arrays with a batch dimension specified using the `dataFormat` argument	Numeric array of the same dimensionality as the input images. The spatial and channel dimensions of `snr` are singleton dimensions. There is one SNR measurement for each element along the batch dimension.
Formatted `dlarray` objects with a batch dimension Unformatted `dlarray` objects with a batch dimension specified using the `dataFormat` argument	`dlarray` object of the same dimensionality as the input images. The spatial and channel dimensions of `peaksnr` are singleton dimensions. There is one SNR measurement for each element along the batch dimension.

If A and ref have data type single, then snr has data type single. Otherwise, snr has data type double.

Algorithms

The psnr function implements this equation to calculate PSNR:

$P S N R = 10 \log_{10} (p e a k v a l^{2} / M S E)$

peakval is either specified by the user or taken from the range of the image data type. For example, for an image of data type uint8, the peakval is 255. MSE is the mean square error between A and ref.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

psnr supports the generation of C code (requires MATLAB^® Coder™). For more information, see Code Generation for Image Processing.

GPU Code Generation
Generate CUDA® code for NVIDIA® GPUs using GPU Coder™.

GPU Arrays
Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

This function fully supports GPU arrays. For more information, see Image Processing on a GPU.

Version History

Introduced in R2014a

expand all

R2021a: Calculate metrics of deep learning arrays and specify dimensions of computation

The psnr function now accepts dlarray input for deep learning applications.

This function also supports formatted data with dimension labels of 'S' (spatial), 'C' (channel), and 'B' (batch). For data with a batch dimension, the function returns a separate result for each index along the batch dimension.

R2021a: Support for GPU acceleration

psnr now supports GPU acceleration (requires Parallel Computing Toolbox™).

psnr

Syntax

Description

Examples

Calculate PSNR for Noisy Image Given Original Image as Reference

Calculate PSNR for `dlarray` Input

Calculate PSNR of Images in Image Sequence

Input Arguments

`A` — Image to be analyzed
numeric array | `dlarray` object

`ref` — Reference image
numeric matrix | `dlarray` object

`peakval` — Peak signal level
nonnegative number

`dataFormat` — Dimension labels
string scalar | character vector

Output Arguments

`peaksnr` — PSNR
numeric scalar | numeric array | `dlarray` object

`snr` — Signal-to-noise ratio
numeric scalar | numeric array | `dlarray` object

Algorithms

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

GPU Code Generation
Generate CUDA® code for NVIDIA® GPUs using GPU Coder™.

GPU Arrays
Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

Version History

R2021a: Calculate metrics of deep learning arrays and specify dimensions of computation

R2021a: Support for GPU acceleration

See Also

Topics

psnr

Syntax

Description

Examples

Calculate PSNR for Noisy Image Given Original Image as Reference

Calculate PSNR for dlarray Input

Calculate PSNR of Images in Image Sequence

Input Arguments

A — Image to be analyzed numeric array | dlarray object

ref — Reference image numeric matrix | dlarray object

peakval — Peak signal level nonnegative number

dataFormat — Dimension labels string scalar | character vector

Output Arguments

peaksnr — PSNR numeric scalar | numeric array | dlarray object

snr — Signal-to-noise ratio numeric scalar | numeric array | dlarray object

Algorithms

Extended Capabilities

C/C++ Code Generation Generate C and C++ code using MATLAB® Coder™.

GPU Code Generation Generate CUDA® code for NVIDIA® GPUs using GPU Coder™.

GPU Arrays Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

Version History

R2021a: Calculate metrics of deep learning arrays and specify dimensions of computation

R2021a: Support for GPU acceleration

See Also

Topics

Calculate PSNR for `dlarray` Input

`A` — Image to be analyzed
numeric array | `dlarray` object

`ref` — Reference image
numeric matrix | `dlarray` object

`peakval` — Peak signal level
nonnegative number

`dataFormat` — Dimension labels
string scalar | character vector

`peaksnr` — PSNR
numeric scalar | numeric array | `dlarray` object

`snr` — Signal-to-noise ratio
numeric scalar | numeric array | `dlarray` object

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

GPU Code Generation
Generate CUDA® code for NVIDIA® GPUs using GPU Coder™.

GPU Arrays
Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.