int** ary = new int[sizeY][sizeX]

should be:

int **ary = new int*[sizeY];
for(int i = 0; i < sizeY; ++i) {
    ary[i] = new int[sizeX];
}

and then clean up would be:

for(int i = 0; i < sizeY; ++i) {
    delete [] ary[i];
}
delete [] ary;

int** ary = new int[sizeY][sizeX]

should be:

int **ary = new int*[sizeY];
for(int i = 0; i < sizeY; ++i) {
    ary[i] = new int[sizeX];
}

and then clean up would be:

for(int i = 0; i < sizeY; ++i) {
    delete [] ary[i];
}
delete [] ary;

EDIT: as Dietrich Epp pointed out in the comments this is not exactly a light weight solution. An alternative approach would be to use one large block of memory:

int *ary = new int[sizeX*sizeY];

// ary[i][j] is then rewritten as
ary[i*sizeY+j]