Adjusting gridlines and ticks in matplotlib imshow

Question

I'm trying to plot a matrix of values and would like to add gridlines to make the boundary between values clearer. Unfortunately, imshow decided to locate the tick marks in the middle of each voxel. Is it possible to

a) remove the ticks but leave the label in the same location and
b) add gridlines between the pixel boundaries?

import matplotlib.pyplot as plt
import numpy as np

im = plt.imshow(np.reshape(np.random.rand(100), newshape=(10,10)),
                    interpolation='none', vmin=0, vmax=1, aspect='equal');
ax = plt.gca();
ax.set_xticks(np.arange(0, 10, 1));
ax.set_yticks(np.arange(0, 10, 1));
ax.set_xticklabels(np.arange(1, 11, 1));
ax.set_yticklabels(np.arange(1, 11, 1));

Image without the gridline and with tick marks in the wrong location

ax.grid(color='w', linestyle='-', linewidth=2)

Image with gridlines in the wrong location:

Answer 1

Code for solution as suggested by Serenity:

plt.figure()
im = plt.imshow(np.reshape(np.random.rand(100), newshape=(10,10)),
                interpolation='none', vmin=0, vmax=1, aspect='equal')

ax = plt.gca();

# Major ticks
ax.set_xticks(np.arange(0, 10, 1))
ax.set_yticks(np.arange(0, 10, 1))

# Labels for major ticks
ax.set_xticklabels(np.arange(1, 11, 1))
ax.set_yticklabels(np.arange(1, 11, 1))

# Minor ticks
ax.set_xticks(np.arange(-.5, 10, 1), minor=True)
ax.set_yticks(np.arange(-.5, 10, 1), minor=True)

# Gridlines based on minor ticks
ax.grid(which='minor', color='w', linestyle='-', linewidth=2)

Resulting image: