When convolving an image of size 1500x1500 with a PSF of 11x11, how long does the operation take if each operation is performed in 0.1 ns?

Steps to Solve

1. Determine the dimensions of the image
   The image has dimensions of 1500x1500 pixels. Each pixel is affected by the Point Spread Function (PSF) as it convolves across the image.

2. Calculate the number of operations per pixel
   The PSF has dimensions of 11x11 pixels, which means each pixel in the image requires 11x11 = 121 operations to convolve with the PSF.

3. Calculate the total number of pixels in the image
   The total number of pixels in the image is given by multiplying the width and height of the image:
   $$ \text{Total pixels} = 1500 \times 1500 = 2,250,000 $$

4. Calculate the total number of operations for the convolution
   To find the total number of operations required for the entire image, we multiply the number of pixels by the number of operations per pixel:
   $$ \text{Total operations} = (1500 \times 1500) \times (11 \times 11) = 2,250,000 \times 121 = 272,250,000,000 $$

5. Calculate the total time taken for the convolution
   To find the total time, multiply the total number of operations by the time per operation:
   $$ \text{Total time (ns)} = 272,250,000,000 \times 0.1 = 27,225,000,000 \text{ ns} $$

6. Convert the time to seconds (if needed)
   Since (1 \text{ second} = 1,000,000,000 \text{ nanoseconds}), we can convert the total time to seconds:
   $$ \text{Total time (s)} = \frac{27,225,000,000 \text{ ns}}{1,000,000,000} = 27.225 \text{ seconds} $$